Solve $(3x+2)^2\frac{d^2y}{dx^2}+3(3x+2)\frac{dy}{dx}-36y=3x^2+4x+1$ .

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written 6.3 years ago by

teamques10 ★ 65k

• modified 4.1 years ago

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written 6.2 years ago by

teamques10 ★ 65k

• modified 6.1 years ago

$ \text{ Put 3x +2 =} e^z ,z=log(3x+2) \\ $

$ 9D(D-1)y + 3(3 )Dy - 36y = 3\frac{(e^z - 2) ^2} {3} + 4\frac{(e^z - 2) ^2} {3} + 1\\ $

$ (9D^2- 9D + 9D - 36)y = \frac{1}{3}(e^{2z} - 1) \\ $

$ (9D^2 - 36)y = …

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