29.3.27 problem 81

Internal problem ID [4689]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 3
Problem number : 81
Date solved : Monday, January 27, 2025 at 09:31:45 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 30

dsolve(diff(y(x),x) = a0+a1*y(x)+a2*y(x)^2+a3*y(x)^3,y(x), singsol=all)
 

\[ x -\int _{}^{y \left (x \right )}\frac {1}{\textit {\_a}^{3} \operatorname {a3} +\textit {\_a}^{2} \operatorname {a2} +\textit {\_a} \operatorname {a1} +\operatorname {a0}}d \textit {\_a} +c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.115 (sec). Leaf size: 54

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

\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3 \text {a3}+\text {$\#$1}^2 \text {a2}+\text {$\#$1} \text {a1}+\text {a0}\&,\frac {\log (y(x)-\text {$\#$1})}{3 \text {$\#$1}^2 \text {a3}+2 \text {$\#$1} \text {a2}+\text {a1}}\&\right ]=x+c_1,y(x)\right ] \]