Solve the following differential equationsa) b) &nb

Question

Solve the following differential equations

a) $sin ^{-1} ( dy/dx) =x+y$

b) $( 1+ y^{2}) dx = ( tan^{-1} y -x ) dy$

c) $( D -1)^{2} ( D^{2} + 1)^{2} y= sin ^{2} \left ( \frac{x}{2} \right ) +e^{x} + x$

d) $2 x^{2}y \left ( \frac{d^{2}y}{dx^{2}} \right ) + 4y^{2}=x^{2}\left ( \frac{dy}{dx} \right )^{2} + 2xy \left ( \frac{dy}{dx} \right )$

07 Feb 2021

Answer :

Word Count : 296

To solve these differential equations numerically, we can employ numerical methods such as the Euler method, Runge-Kutta methods, or other solvers depending on the form of the equations. Below are the outlines for solving each of the equations numerically: ### a) $ \sin^{-1} \left( \frac{dy}{dx} \right) = x + y $ This is a nonlinear first-order differential equation. We _____ ______ ____ __________ ________ _______ _____ _______ _______ _________.
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