Internal problem ID [3195]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 16
Problem number: 449.
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 (2 x -y+4\right ) y^{\prime }+5+x -2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 182
dsolve((4+2*x-y(x))*diff(y(x),x)+5+x-2*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = 2-\frac {\left (x +1\right ) \left (c_{1}^{2} \left (-\frac {\left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +1\right )^{2}-1}+27 c_{1} \left (x +1\right )\right )^{\frac {1}{3}}}{6 c_{1} \left (x +1\right )}-\frac {1}{2 c_{1} \left (x +1\right ) \left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +1\right )^{2}-1}+27 c_{1} \left (x +1\right )\right )^{\frac {1}{3}}}+\frac {i \sqrt {3}\, \left (\frac {\left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +1\right )^{2}-1}+27 c_{1} \left (x +1\right )\right )^{\frac {1}{3}}}{3 c_{1} \left (x +1\right )}-\frac {1}{c_{1} \left (x +1\right ) \left (3 \sqrt {3}\, \sqrt {27 c_{1}^{2} \left (x +1\right )^{2}-1}+27 c_{1} \left (x +1\right )\right )^{\frac {1}{3}}}\right )}{2}\right )+c_{1}^{2}\right )}{c_{1}^{2}} \]
✓ Solution by Mathematica
Time used: 0.183 (sec). Leaf size: 629
DSolve[(4+2 x-y[x])y'[x]+5+x-2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 (x+2)+\frac {3 (x+1)}{\frac {1}{\sqrt [3]{-e^{\frac {3 c_1}{4}} (x+1)^4+2 e^{\frac {3 c_1}{8}} (x+1)^2+\sqrt {e^{\frac {3 c_1}{8}} (x+1)^2 \left (-1+e^{\frac {3 c_1}{8}} (x+1)^2\right ){}^3}-1}}-\frac {\sqrt [3]{-e^{\frac {3 c_1}{4}} (x+1)^4+2 e^{\frac {3 c_1}{8}} (x+1)^2+\sqrt {e^{\frac {3 c_1}{8}} (x+1)^2 \left (-1+e^{\frac {3 c_1}{8}} (x+1)^2\right ){}^3}-1}}{(x+1)^2 \cosh \left (\frac {3 c_1}{8}\right )+(x+1)^2 \sinh \left (\frac {3 c_1}{8}\right )-1}-1} \\ y(x)\to 2 \left (x+\frac {3 (x+1)}{\frac {-1-i \sqrt {3}}{\sqrt [3]{-e^{\frac {3 c_1}{4}} (x+1)^4+2 e^{\frac {3 c_1}{8}} (x+1)^2+\sqrt {e^{\frac {3 c_1}{8}} (x+1)^2 \left (-1+e^{\frac {3 c_1}{8}} (x+1)^2\right ){}^3}-1}}+\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-e^{\frac {3 c_1}{4}} (x+1)^4+2 e^{\frac {3 c_1}{8}} (x+1)^2+\sqrt {e^{\frac {3 c_1}{8}} (x+1)^2 \left (-1+e^{\frac {3 c_1}{8}} (x+1)^2\right ){}^3}-1}}{(x+1)^2 \cosh \left (\frac {3 c_1}{8}\right )+(x+1)^2 \sinh \left (\frac {3 c_1}{8}\right )-1}-2}+2\right ) \\ y(x)\to 2 \left (x+\frac {3 (x+1)}{\frac {i \left (\sqrt {3}+i\right )}{\sqrt [3]{-e^{\frac {3 c_1}{4}} (x+1)^4+2 e^{\frac {3 c_1}{8}} (x+1)^2+\sqrt {e^{\frac {3 c_1}{8}} (x+1)^2 \left (-1+e^{\frac {3 c_1}{8}} (x+1)^2\right ){}^3}-1}}+\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-e^{\frac {3 c_1}{4}} (x+1)^4+2 e^{\frac {3 c_1}{8}} (x+1)^2+\sqrt {e^{\frac {3 c_1}{8}} (x+1)^2 \left (-1+e^{\frac {3 c_1}{8}} (x+1)^2\right ){}^3}-1}}{(x+1)^2 \cosh \left (\frac {3 c_1}{8}\right )+(x+1)^2 \sinh \left (\frac {3 c_1}{8}\right )-1}-2}+2\right ) \\ \end{align*}