29.34.13 problem 1015

Internal problem ID [5584]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 34
Problem number : 1015
Date solved : Monday, January 27, 2025 at 12:12:46 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{3}&=b x +a \end{align*}

✓ Solution by Maple

Time used: 0.056 (sec). Leaf size: 88

dsolve(diff(y(x),x)^3 = b*x+a,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {\left (3 b x +3 a \right ) \left (b x +a \right )^{{1}/{3}}+4 c_{1} b}{4 b} \\ y \left (x \right ) &= \frac {-3 \left (1+i \sqrt {3}\right ) \left (b x +a \right )^{{4}/{3}}+8 c_{1} b}{8 b} \\ y \left (x \right ) &= \frac {3 \left (i \sqrt {3}-1\right ) \left (b x +a \right )^{{4}/{3}}+8 c_{1} b}{8 b} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 80

DSolve[(D[y[x],x])^3 ==a+b x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {3 (a+b x)^{4/3}}{4 b}+c_1 \\ y(x)\to -\frac {3 \sqrt [3]{-1} (a+b x)^{4/3}}{4 b}+c_1 \\ y(x)\to \frac {3 (-1)^{2/3} (a+b x)^{4/3}}{4 b}+c_1 \\ \end{align*}