75.12.29 problem 303

Internal problem ID [16895]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 303
Date solved : Tuesday, January 28, 2025 at 09:40:03 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.098 (sec). Leaf size: 79

dsolve((3*(x+y(x))+a^2)*diff(y(x),x)=4*(x+y(x))+b^2,y(x), singsol=all)
 

\[ y = \frac {\left (4 a^{2}-3 b^{2}\right ) \operatorname {LambertW}\left (\frac {3 \,{\mathrm e}^{\frac {3 a^{2}+3 b^{2}-49 c_{1} +49 x}{4 a^{2}-3 b^{2}}}}{4 a^{2}-3 b^{2}}\right )}{21}-\frac {a^{2}}{7}-\frac {b^{2}}{7}-x \]

✓ Solution by Mathematica

Time used: 60.053 (sec). Leaf size: 97

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

\[ y(x)\to \frac {1}{21} \left (-3 \left (a^2+b^2+7 x\right )+\left (4 a^2-3 b^2\right ) W\left (-4 \left (2^{\frac {3 b^2}{2 a^2}-2} e^{\frac {49 x-3 b^2 (-1+c_1)}{4 a^2}-1+c_1}\right ){}^{\frac {4 a^2}{4 a^2-3 b^2}}\right )\right ) \]