15.6.12 problem 12

Internal problem ID [2969]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 12
Date solved : Monday, January 27, 2025 at 07:04:51 AM
CAS classification : [_linear]

\begin{align*} x^{2} y^{\prime }+y-2 y x -2 x^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

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

\[ y = x^{2} \left (2+c_{1} {\mathrm e}^{\frac {1}{x}}\right ) \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 19

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

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