Internal problem ID [4119]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 883.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_rational, _dAlembert]
\[ \boxed {\left (5+3 x \right ) {y^{\prime }}^{2}-\left (3+3 y\right ) y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 249
dsolve((5+3*x)*diff(y(x),x)^2-(3+3*y(x))*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\begin{align*} \frac {-108 \left (x -\frac {3 y \left (x \right )}{2}-\frac {\sqrt {9+9 y \left (x \right )^{2}+\left (-12 x -2\right ) y \left (x \right )}}{2}+\frac {1}{6}\right ) \left (c_{1} -\frac {\operatorname {expIntegral}_{1}\left (\frac {-9 y \left (x \right )-9-3 \sqrt {9+9 y \left (x \right )^{2}+\left (-12 x -2\right ) y \left (x \right )}}{10+6 x}\right )}{2}\right ) {\mathrm e}^{\frac {-9 y \left (x \right )-9-3 \sqrt {9+9 y \left (x \right )^{2}+\left (-12 x -2\right ) y \left (x \right )}}{10+6 x}}+18 x^{2}+6 x -40}{30+18 x} &= 0 \\ \frac {108 \left (x -\frac {3 y \left (x \right )}{2}+\frac {\sqrt {9+9 y \left (x \right )^{2}+\left (-12 x -2\right ) y \left (x \right )}}{2}+\frac {1}{6}\right ) \left (c_{1} +\frac {\operatorname {expIntegral}_{1}\left (\frac {-9 y \left (x \right )-9+3 \sqrt {9+9 y \left (x \right )^{2}+\left (-12 x -2\right ) y \left (x \right )}}{10+6 x}\right )}{2}\right ) {\mathrm e}^{\frac {-9 y \left (x \right )-9+3 \sqrt {9+9 y \left (x \right )^{2}+\left (-12 x -2\right ) y \left (x \right )}}{10+6 x}}+18 x^{2}+6 x -40}{30+18 x} &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.709 (sec). Leaf size: 106
DSolve[(5+3 x) (y'[x])^2-(3+3 y[x])y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\left \{x=\frac {e^{-3 K[1]} (3 K[1]-1) \left ((9-27 K[1]) \operatorname {ExpIntegralEi}(3 K[1])+4 e^{3 K[1]}\right )}{9 K[1]-3}+c_1 e^{-3 K[1]} (3 K[1]-1),y(x)=\frac {3 x K[1]^2}{3 K[1]-1}+\frac {5 K[1]^2-3 K[1]}{3 K[1]-1}\right \},\{y(x),K[1]\}\right ] \]