69.1.13 problem 13

Internal problem ID [14166]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 06:18:30 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 12

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

\[ y = a +{\mathrm e}^{\frac {1}{x}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 20

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

\begin{align*} y(x)\to a+c_1 e^{\frac {1}{x}} \\ y(x)\to a \\ \end{align*}