60.1.92 problem 92

Internal problem ID [10106]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 92
Date solved : Monday, January 27, 2025 at 06:27:43 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }-y-x^{2} \sin \left (x \right )&=0 \end{align*}

✓ Solution by Maple

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

dsolve(x*diff(y(x),x) - y(x) - x^2*sin(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 20

DSolve[x*D[y[x],x] - y[x] - x^2*Sin[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \left (\int _1^x\sin (K[1])dK[1]+c_1\right ) \]