Solve the following ordinary differential equations:a) b)

Question

Solve the following ordinary differential equations:

a) $\left(2yx^{2}+4\right)\frac{dy}{dx}+\left(2y^{2}-3\right)=0$

b) $\frac{d^{2}y}{dx^{2}}-6\frac{dy}{dx}+13y=0$ for y(o) = 2, $y\left(\frac{\pi}{4}\right)=3$ .

22 Jan 2025

Answer :

Word Count : 93

a) $\displaystyle(2yx^{2}+4)\frac{dy}{dx}+(2y^{2}-3)=0$. Rearrange as $$ \frac{dx}{dy}=-\frac{2yx^{2}+4}{2y^{2}-3}=-\frac{2y}{2y^{2}-3}x^{2}-\frac{4}{2y^{2}-3}. $$ Put the terms with $x$ on one side __________ ________ _______ _________ ________.
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