Internal problem ID [1983]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number: Problem 14.5 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (1-x^{2}\right ) y^{\prime }+4 y x -\left (1-x^{2}\right )^{\frac {3}{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve((1-x^2)*diff(y(x),x)+2*x*y(x)+2*x*y(x)=(1-x^2)^(3/2),y(x), singsol=all)
\[ y \relax (x ) = \left (x^{4}-2 x^{2}+1\right ) c_{1}-\sqrt {-x^{2}+1}\, x \left (x^{2}-1\right ) \]
✓ Solution by Mathematica
Time used: 0.121 (sec). Leaf size: 29
DSolve[(1-x^2)*y'[x]+2*x*y[x]+2*x*y[x]==(1-x^2)^(3/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (x^2-1\right )^2 \left (\frac {x}{\sqrt {1-x^2}}+c_1\right ) \\ \end{align*}