29.11.14 problem 305

Internal problem ID [4905]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 305
Date solved : Monday, January 27, 2025 at 09:47:27 AM
CAS classification : [_linear]

\begin{align*} \left (a^{2}+x^{2}\right ) y^{\prime }&=b +y x \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

dsolve((a^2+x^2)*diff(y(x),x) = b+x*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\sqrt {a^{2}+x^{2}}\, c_{1} a^{2}+b x}{a^{2}} \]

✓ Solution by Mathematica

Time used: 0.078 (sec). Leaf size: 26

DSolve[(a^2+x^2)D[y[x],x]==b+x y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {b x}{a^2}+c_1 \sqrt {a^2+x^2} \]