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Solve the $xy(1+xy^2)\dfrac {dy}{dx}=1$
engineering mathematics updated 4.3 years ago by krithikkm200 • 10
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Use the method of variation of parameter to solve $\dfrac {d^2y}{dx^2}+5\dfrac{dy}{dx}+6y =e^{-2x}\sec^2x(1+2\tan x) $
engineering mathematics updated 4.3 years ago by krithikkm200 • 10
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$\dfrac {d^2y}{dx^2}+2y=x^2e^{3x}+e^x-\cos 2x$
engineering mathematics updated 4.3 years ago by krithikkm200 • 10
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Find $A^5- 4A^4-7 A^3+11 A^2-A-10I$ in terms of A using Cayley Hamilton theorem for A=$ \left[ \begin{array}{ccc} 1 & 4 \\ 2 & 3 \end{array}\right] $
engineering mathematics updated 4.4 years ago by phenjoisilab • 0
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IF A = $ \left[ \begin{array}{ccc} 2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2 \end{array}\right] $ Find the characteristics roots of A and $A^3+1$.
engineering mathematics updated 4.4 years ago by phenjoisilab • 0
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Find the eigen values and eigen vectors of matrix A = $\begin{bmatrix} 2 & 1 & 1 \\ 2 & 3 & 2 \\ 3 & 3 & 4 \end{bmatrix}$
engineering mathematics updated 4.4 years ago by phenjoisilab • 0
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If A = $ \left[ \begin{array}{ccc} -1 & 4 \\ 2 & 1 \end{array}\right] $ then prove that 3tanA=Atan3.
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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Show that the matrix A=$ \left[ \begin{array}{ccc} 8 & -6 & 2 \\ -6 & 7 & -4 \\ 2 & -4 & 3 \end{array}\right] $ is diagonalisable. Find the diagonal form and transforming matrix.
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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Find the eigen values of the adjoint of the matrix. $ \left[ \begin{array}{ccc} 2 & 0 & -1 \\ 0 & 2 & 0 \\ -1 & 0 & 2 \end{array}\right] $
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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Find $A^{50}$ if A= $ \left[ \begin{array}{ccc} 2 & 1 \\ 1 & 2 \end{array}\right] $
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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Find the characteristic equation of the matrix A given below and hence find the matrix represented by $A^6-6A^5+9A^4+4A^3-12A^2+2A-1$ where A is given below.
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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Find the total length of the loop of the curve $ay^2=(x+7)(x+4)^2$
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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Evaluate $\int\limits_0^2 x^4(8-x^3)^{\dfrac{-1}3}$
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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Basic partial derivatives : If $u \; = \; x^y , \; find \; \frac{\partial^3 u}{\partial x \partial y \partial x} $
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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Evaluate $\int\limits_0^{\dfrac \pi2} \dfrac {dx}{a^2\sin^2x + b^2\cos^2x}----- $ eq(1) and show that
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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Change to polar coordinate and evaluate $\int\limits_0^{2a}\int\limits_0^{\sqrt{2ax-x^2}}\dfrac{x}{\sqrt{x^2+y^2}}$dydx
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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Prove thata $\int\limits_0^{\infty}\cos\lambda x (e^{-ax}-e^{-bx}) dx=\dfrac 12 \log\Bigg(\dfrac {b^2+\lambda^2}{a^2+\lambda^2}\Bigg),a>0,b>0$ using DUIS rule
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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Find the length of one arc of the cycloid $x =a(\theta-\sin\theta)$ and $y=a(1+\cos\theta)$
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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Solve $(xy^2-e^{1/x3})dx-x^2y\space dy=0$
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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Evaluate $\int\limits_0^{\infty}\dfrac {x^4}{4^x}dx$
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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Solve $(1+e^{\dfrac xy})dx+e^{\dfrac xy}(1-\dfrac xy)dy=0$
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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PT $\int\limits_0^{\infty}\dfrac {x^{m-1}}{(a+bx)^{m+n}}=\dfrac 1{a^nb^m}\beta(m,n)$
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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$\int\limits_0^{\infty}\dfrac {\log(1+ax^2)}{x^2}dx=\pi\sqrt a..$ where $a > 0$
engineering mathematics updated 4.4 years ago by krithikkm200 • 10
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Solve $(x^2-4xy-2y^2)dx + (y^2-4xy-2x^2)dy=0$
engineering mathematics updated 4.4 years ago by phenjoisilab • 0
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Solve $\dfrac {dy}{dx} + x(x+y)=x^3(x+y)^3-1$
engineering mathematics updated 4.4 years ago by phenjoisilab • 0
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