69.1.33 problem 50

Internal problem ID [14186]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 50
Date solved : Tuesday, January 28, 2025 at 06:19:46 AM
CAS classification : [_linear]

\begin{align*} x +2 y+1-\left (2 x -3\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

dsolve((x+2*y(x)+1)-(2*x-3)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -\frac {5}{4}+\frac {\left (2 x -3\right ) \ln \left (2 x -3\right )}{4}+\left (2 x -3\right ) c_{1} \]

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 35

DSolve[(x+2*y[x]+1)-(2*x-3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (2 x-3) \left (\frac {x+1}{6-4 x}+\frac {1}{4} \log (6-4 x)+c_1\right ) \]