69.1.68 problem 96

Internal problem ID [14221]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 96
Date solved : Tuesday, January 28, 2025 at 06:22:29 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 9

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

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

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 16

DSolve[y[x]==x*D[y[x],x]+D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 (x+1) \\ y(x)\to 0 \\ \end{align*}