Internal problem ID [15165]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (3 y+3 x +a^{2}\right ) y^{\prime }-4 y=b^{2}+4 x} \]
✓ Solution by Maple
Time used: 0.015 (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: 60.042 (sec). Leaf size: 97
DSolve[(3*(x+y[x])+a^2)*y'[x]==4*(x+y[x])+b^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{21} \left (-3 \left (a^2+b^2+7 x\right )+\left (4 a^2-3 b^2\right ) W\left (-4 \left (2^{\frac {3 b^2}{2 a^2}-2} e^{\frac {49 x-3 b^2 (-1+c_1)}{4 a^2}-1+c_1}\right ){}^{\frac {4 a^2}{4 a^2-3 b^2}}\right )\right ) \]