29.35.12 problem 1044

Internal problem ID [5610]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1044
Date solved : Monday, January 27, 2025 at 12:24:20 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{3}+\operatorname {a0} {y^{\prime }}^{2}+\operatorname {a1} y^{\prime }+\operatorname {a2} +\operatorname {a3} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.132 (sec). Leaf size: 975

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 )^{{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 )^{{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 )^{{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 )^{{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 )^{{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 )^{{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 )^{{1}/{3}}+2 \operatorname {a0}^{2}-6 \operatorname {a1}}d \textit {\_a} \right )+i \left (-c_{1} +x \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 )^{{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 )^{{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 )^{{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 )^{{1}/{3}}-2 \operatorname {a0}^{2}+6 \operatorname {a1}}d \textit {\_a} \right )+i \left (-c_{1} +x \right ) \sqrt {3}-x +c_{1}}{i \sqrt {3}-1} &= 0 \\ \end{align*}

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[(D[y[x],x])^3 + a0*(D[y[x],x])^2 +a1*D[y[x],x]+a2 +a3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Timed out