Internal problem ID [4266]
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]
\[ \boxed {{y^{\prime }}^{3}+\operatorname {a0} {y^{\prime }}^{2}+\operatorname {a1} y^{\prime }+\operatorname {a3} y=-\operatorname {a2}} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 981
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 -6 \left (\int _{}^{y \left (x \right )}\frac {\left (36 \operatorname {a1} \operatorname {a0} -108 \operatorname {a3} \textit {\_a} -108 \operatorname {a2} -8 \operatorname {a0}^{3}+12 \sqrt {12 \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0}^{3}-3 \operatorname {a1}^{2} \operatorname {a0}^{2}-54 \operatorname {a1} \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0} +81 \textit {\_a}^{2} \operatorname {a3}^{2}+162 \textit {\_a} \operatorname {a2} \operatorname {a3} +12 \operatorname {a1}^{3}+81 \operatorname {a2}^{2}}\right )^{\frac {1}{3}}}{\left (36 \operatorname {a1} \operatorname {a0} -108 \operatorname {a3} \textit {\_a} -108 \operatorname {a2} -8 \operatorname {a0}^{3}+12 \sqrt {12 \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0}^{3}-3 \operatorname {a1}^{2} \operatorname {a0}^{2}-54 \operatorname {a1} \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0} +81 \textit {\_a}^{2} \operatorname {a3}^{2}+162 \textit {\_a} \operatorname {a2} \operatorname {a3} +12 \operatorname {a1}^{3}+81 \operatorname {a2}^{2}}\right )^{\frac {2}{3}}-2 \operatorname {a0} \left (36 \operatorname {a1} \operatorname {a0} -108 \operatorname {a3} \textit {\_a} -108 \operatorname {a2} -8 \operatorname {a0}^{3}+12 \sqrt {12 \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0}^{3}-3 \operatorname {a1}^{2} \operatorname {a0}^{2}-54 \operatorname {a1} \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0} +81 \textit {\_a}^{2} \operatorname {a3}^{2}+162 \textit {\_a} \operatorname {a2} \operatorname {a3} +12 \operatorname {a1}^{3}+81 \operatorname {a2}^{2}}\right )^{\frac {1}{3}}+4 \operatorname {a0}^{2}-12 \operatorname {a1}}d \textit {\_a} \right )-c_{1} &= 0 \\ \frac {-12 \left (\int _{}^{y \left (x \right )}\frac {\left (36 \operatorname {a1} \operatorname {a0} -108 \operatorname {a3} \textit {\_a} -108 \operatorname {a2} -8 \operatorname {a0}^{3}+12 \sqrt {12 \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0}^{3}-3 \operatorname {a1}^{2} \operatorname {a0}^{2}-54 \operatorname {a1} \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0} +81 \textit {\_a}^{2} \operatorname {a3}^{2}+162 \textit {\_a} \operatorname {a2} \operatorname {a3} +12 \operatorname {a1}^{3}+81 \operatorname {a2}^{2}}\right )^{\frac {1}{3}}}{i \left (\operatorname {a0} \left (36 \operatorname {a1} \operatorname {a0} -108 \operatorname {a3} \textit {\_a} -108 \operatorname {a2} -8 \operatorname {a0}^{3}+12 \sqrt {12 \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0}^{3}-3 \operatorname {a1}^{2} \operatorname {a0}^{2}-54 \operatorname {a1} \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0} +81 \textit {\_a}^{2} \operatorname {a3}^{2}+162 \textit {\_a} \operatorname {a2} \operatorname {a3} +12 \operatorname {a1}^{3}+81 \operatorname {a2}^{2}}\right )^{\frac {1}{3}}+2 \operatorname {a0}^{2}-6 \operatorname {a1} \right ) \sqrt {3}-\left (36 \operatorname {a1} \operatorname {a0} -108 \operatorname {a3} \textit {\_a} -108 \operatorname {a2} -8 \operatorname {a0}^{3}+12 \sqrt {12 \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0}^{3}-3 \operatorname {a1}^{2} \operatorname {a0}^{2}-54 \operatorname {a1} \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0} +81 \textit {\_a}^{2} \operatorname {a3}^{2}+162 \textit {\_a} \operatorname {a2} \operatorname {a3} +12 \operatorname {a1}^{3}+81 \operatorname {a2}^{2}}\right )^{\frac {2}{3}}-\operatorname {a0} \left (36 \operatorname {a1} \operatorname {a0} -108 \operatorname {a3} \textit {\_a} -108 \operatorname {a2} -8 \operatorname {a0}^{3}+12 \sqrt {12 \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0}^{3}-3 \operatorname {a1}^{2} \operatorname {a0}^{2}-54 \operatorname {a1} \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0} +81 \textit {\_a}^{2} \operatorname {a3}^{2}+162 \textit {\_a} \operatorname {a2} \operatorname {a3} +12 \operatorname {a1}^{3}+81 \operatorname {a2}^{2}}\right )^{\frac {1}{3}}+2 \operatorname {a0}^{2}-6 \operatorname {a1}}d \textit {\_a} \right )+i \left (x -c_{1} \right ) \sqrt {3}+x -c_{1}}{1+i \sqrt {3}} &= 0 \\ \frac {-12 \left (\int _{}^{y \left (x \right )}\frac {\left (36 \operatorname {a1} \operatorname {a0} -108 \operatorname {a3} \textit {\_a} -108 \operatorname {a2} -8 \operatorname {a0}^{3}+12 \sqrt {12 \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0}^{3}-3 \operatorname {a1}^{2} \operatorname {a0}^{2}-54 \operatorname {a1} \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0} +81 \textit {\_a}^{2} \operatorname {a3}^{2}+162 \textit {\_a} \operatorname {a2} \operatorname {a3} +12 \operatorname {a1}^{3}+81 \operatorname {a2}^{2}}\right )^{\frac {1}{3}}}{i \left (\operatorname {a0} \left (36 \operatorname {a1} \operatorname {a0} -108 \operatorname {a3} \textit {\_a} -108 \operatorname {a2} -8 \operatorname {a0}^{3}+12 \sqrt {12 \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0}^{3}-3 \operatorname {a1}^{2} \operatorname {a0}^{2}-54 \operatorname {a1} \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0} +81 \textit {\_a}^{2} \operatorname {a3}^{2}+162 \textit {\_a} \operatorname {a2} \operatorname {a3} +12 \operatorname {a1}^{3}+81 \operatorname {a2}^{2}}\right )^{\frac {1}{3}}+2 \operatorname {a0}^{2}-6 \operatorname {a1} \right ) \sqrt {3}+\left (36 \operatorname {a1} \operatorname {a0} -108 \operatorname {a3} \textit {\_a} -108 \operatorname {a2} -8 \operatorname {a0}^{3}+12 \sqrt {12 \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0}^{3}-3 \operatorname {a1}^{2} \operatorname {a0}^{2}-54 \operatorname {a1} \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0} +81 \textit {\_a}^{2} \operatorname {a3}^{2}+162 \textit {\_a} \operatorname {a2} \operatorname {a3} +12 \operatorname {a1}^{3}+81 \operatorname {a2}^{2}}\right )^{\frac {2}{3}}+\operatorname {a0} \left (36 \operatorname {a1} \operatorname {a0} -108 \operatorname {a3} \textit {\_a} -108 \operatorname {a2} -8 \operatorname {a0}^{3}+12 \sqrt {12 \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0}^{3}-3 \operatorname {a1}^{2} \operatorname {a0}^{2}-54 \operatorname {a1} \left (\operatorname {a3} \textit {\_a} +\operatorname {a2} \right ) \operatorname {a0} +81 \textit {\_a}^{2} \operatorname {a3}^{2}+162 \textit {\_a} \operatorname {a2} \operatorname {a3} +12 \operatorname {a1}^{3}+81 \operatorname {a2}^{2}}\right )^{\frac {1}{3}}-2 \operatorname {a0}^{2}+6 \operatorname {a1}}d \textit {\_a} \right )+i \left (x -c_{1} \right ) \sqrt {3}-x +c_{1}}{-1+i \sqrt {3}} &= 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