29.6.3 problem 149

Internal problem ID [4749]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 6
Problem number : 149
Date solved : Monday, January 27, 2025 at 09:36:20 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 12

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

\[ y \left (x \right ) = \left (-\cos \left (x \right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 14

DSolve[x D[y[x],x]==x^2 Sin[x]+y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x (-\cos (x)+c_1) \]