Internal problem ID [3213]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 17
Problem number: 467.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (x +2 y+1\right ) y^{\prime }+7+x -4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 254
dsolve((1+x+2*y(x))*diff(y(x),x)+7+x-4*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = 1+\frac {\left (12 \sqrt {3}\, \left (3+x \right ) \sqrt {\frac {\left (3+x \right ) \left (27 \left (3+x \right ) c_{1}-32\right )}{c_{1}}}\, c_{1}^{2}+108 \left (3+x \right )^{2} c_{1}^{2}-576 \left (3+x \right ) c_{1}+512\right )^{\frac {1}{3}}}{12 c_{1}}-\frac {4 \left (3 \left (3+x \right ) c_{1}-4\right )}{3 c_{1} \left (12 \sqrt {3}\, \left (3+x \right ) \sqrt {\frac {\left (3+x \right ) \left (27 \left (3+x \right ) c_{1}-32\right )}{c_{1}}}\, c_{1}^{2}+108 \left (3+x \right )^{2} c_{1}^{2}-576 \left (3+x \right ) c_{1}+512\right )^{\frac {1}{3}}}+\frac {3 \left (3+x \right ) c_{1}-4}{3 c_{1}}-\frac {i \sqrt {3}\, \left (\frac {\left (12 \sqrt {3}\, \left (3+x \right ) \sqrt {\frac {\left (3+x \right ) \left (27 \left (3+x \right ) c_{1}-32\right )}{c_{1}}}\, c_{1}^{2}+108 \left (3+x \right )^{2} c_{1}^{2}-576 \left (3+x \right ) c_{1}+512\right )^{\frac {1}{3}}}{6 c_{1}}+\frac {8 \left (3+x \right ) c_{1}-\frac {32}{3}}{c_{1} \left (12 \sqrt {3}\, \left (3+x \right ) \sqrt {\frac {\left (3+x \right ) \left (27 \left (3+x \right ) c_{1}-32\right )}{c_{1}}}\, c_{1}^{2}+108 \left (3+x \right )^{2} c_{1}^{2}-576 \left (3+x \right ) c_{1}+512\right )^{\frac {1}{3}}}\right )}{2} \]
✓ Solution by Mathematica
Time used: 60.121 (sec). Leaf size: 2617
DSolve[(1+x+2 y[x])y'[x]+7+x-4 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
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