18.1.7 problem Problem 14.5 (a)

Internal problem ID [3463]
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)
Date solved : Monday, January 27, 2025 at 07:37:44 AM
CAS classification : [_linear]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+4 y x&=\left (-x^{2}+1\right )^{{3}/{2}} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 42

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)
 

\[ y \left (x \right ) = c_{1} x^{4}-x^{3} \sqrt {-x^{2}+1}-2 c_{1} x^{2}+x \sqrt {-x^{2}+1}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.092 (sec). Leaf size: 29

DSolve[(1-x^2)*D[y[x],x]+2*x*y[x]+2*x*y[x]==(1-x^2)^(3/2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (x^2-1\right )^2 \left (\frac {x}{\sqrt {1-x^2}}+c_1\right ) \]