77.1.13 problem 27 (page 32)

Internal problem ID [17903]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 27 (page 32)
Date solved : Tuesday, January 28, 2025 at 11:11:53 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x +2 y+1\right ) y^{\prime }&=2 x +4 y+3 \end{align*}

✓ Solution by Maple

Time used: 0.086 (sec). Leaf size: 21

dsolve((x+2*y(x)+1)*diff(y(x),x)=2*x+4*y(x)+3,y(x), singsol=all)
 

\[ y = -\frac {x}{2}-\frac {\operatorname {LambertW}\left (-\frac {c_{1} {\mathrm e}^{-\frac {7}{2}-\frac {25 x}{2}}}{2}\right )}{5}-\frac {7}{10} \]

✓ Solution by Mathematica

Time used: 4.075 (sec). Leaf size: 43

DSolve[(x+2*y[x]+1)*D[y[x],x]==2*x+4*y[x]+3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{10} \left (-2 W\left (-e^{-\frac {25 x}{2}-1+c_1}\right )-5 x-7\right ) \\ y(x)\to \frac {1}{10} (-5 x-7) \\ \end{align*}