Internal problem ID [3758]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1044.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}+\mathit {a0} \left (y^{\prime }\right )^{2}+\mathit {a1} y^{\prime }+\mathit {a2} +\mathit {a3} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.266 (sec). Leaf size: 1027
dsolve(diff(y(x),x)^3+a0*diff(y(x),x)^2+a1*diff(y(x),x)+a2+a3*y(x) = 0,y(x), singsol=all)
\begin{align*} x -\left (\int _{}^{y \relax (x )}\frac {6 \left (36 \mathit {a1} \mathit {a0} -108 \mathit {a3} \textit {\_a} -108 \mathit {a2} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {1}{3}}}{\left (36 \mathit {a1} \mathit {a0} -108 \mathit {a3} \textit {\_a} -108 \mathit {a2} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {2}{3}}-2 \mathit {a0} \left (36 \mathit {a1} \mathit {a0} -108 \mathit {a3} \textit {\_a} -108 \mathit {a2} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {1}{3}}+4 \mathit {a0}^{2}-12 \mathit {a1}}d \textit {\_a} \right )-c_{1} = 0 \\ x -\left (\int _{}^{y \relax (x )}\frac {12 \left (36 \mathit {a1} \mathit {a0} -108 \mathit {a3} \textit {\_a} -108 \mathit {a2} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {1}{3}}}{\left (1+i \sqrt {3}\right ) \left (i \sqrt {3}\, \left (36 \mathit {a1} \mathit {a0} -108 \mathit {a3} \textit {\_a} -108 \mathit {a2} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {1}{3}} \mathit {a0} +2 i \sqrt {3}\, \mathit {a0}^{2}-6 i \sqrt {3}\, \mathit {a1} -\left (36 \mathit {a1} \mathit {a0} -108 \mathit {a3} \textit {\_a} -108 \mathit {a2} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {2}{3}}-\mathit {a0} \left (36 \mathit {a1} \mathit {a0} -108 \mathit {a3} \textit {\_a} -108 \mathit {a2} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {1}{3}}+2 \mathit {a0}^{2}-6 \mathit {a1} \right )}d \textit {\_a} \right )-c_{1} = 0 \\ x -\left (\int _{}^{y \relax (x )}\frac {12 \left (36 \mathit {a1} \mathit {a0} -108 \mathit {a3} \textit {\_a} -108 \mathit {a2} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {1}{3}}}{\left (-1+i \sqrt {3}\right ) \left (i \sqrt {3}\, \left (36 \mathit {a1} \mathit {a0} -108 \mathit {a3} \textit {\_a} -108 \mathit {a2} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {1}{3}} \mathit {a0} +2 i \sqrt {3}\, \mathit {a0}^{2}-6 i \sqrt {3}\, \mathit {a1} +\left (36 \mathit {a1} \mathit {a0} -108 \mathit {a3} \textit {\_a} -108 \mathit {a2} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {2}{3}}+\mathit {a0} \left (36 \mathit {a1} \mathit {a0} -108 \mathit {a3} \textit {\_a} -108 \mathit {a2} -8 \mathit {a0}^{3}+12 \sqrt {12 \textit {\_a} \,\mathit {a0}^{3} \mathit {a3} +81 \textit {\_a}^{2} \mathit {a3}^{2}-54 \textit {\_a} \mathit {a0} \mathit {a1} \mathit {a3} +12 \mathit {a2} \,\mathit {a0}^{3}-3 \mathit {a1}^{2} \mathit {a0}^{2}+162 \textit {\_a} \mathit {a2} \mathit {a3} -54 \mathit {a1} \mathit {a0} \mathit {a2} +12 \mathit {a1}^{3}+81 \mathit {a2}^{2}}\right )^{\frac {1}{3}}-2 \mathit {a0}^{2}+6 \mathit {a1} \right )}d \textit {\_a} \right )-c_{1} = 0 \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(y'[x])^3 + a0 (y'[x])^2 +a1 y'[x]+a2 +a3 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out