29.12.34 problem 353

Internal problem ID [4953]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 353
Date solved : Monday, January 27, 2025 at 09:55:44 AM
CAS classification : [_linear]

\begin{align*} x \left (x^{2}+1\right ) y^{\prime }&=a \,x^{2}+y \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(x*(x^2+1)*diff(y(x),x) = a*x^2+y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 23

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

\[ y(x)\to \frac {x (a \text {arcsinh}(x)+c_1)}{\sqrt {x^2+1}} \]