69.1.46 problem 65

Internal problem ID [14199]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 65
Date solved : Tuesday, January 28, 2025 at 06:21:37 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {\left (1-2 x \right ) y}{x^{2}}-1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 16

dsolve(diff(y(x),x)+(1-2*x)/x^2*y(x)-1=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 21

DSolve[D[y[x],x]+(1-2*x)/x^2*y[x]-1==0,y[x],x,IncludeSingularSolutions -> True]
 

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