82.13.4 problem Ex. 4

Internal problem ID [18804]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter III. Equations of the first order but not of the first degree. Problems at page 32
Problem number : Ex. 4
Date solved : Tuesday, January 28, 2025 at 12:18:43 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{3}&=a \,x^{4} \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 60

dsolve(diff(y(x),x)^3=a*x^4,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {3 x^{2} \left (a x \right )^{{1}/{3}}}{7}+c_{1} \\ y \left (x \right ) &= -\frac {3 x^{2} \left (1+i \sqrt {3}\right ) \left (a x \right )^{{1}/{3}}}{14}+c_{1} \\ y \left (x \right ) &= \frac {3 x^{2} \left (i \sqrt {3}-1\right ) \left (a x \right )^{{1}/{3}}}{14}+c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 74

DSolve[D[y[x],x]^3==a*x^4,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {3}{7} \sqrt [3]{a} x^{7/3}+c_1 \\ y(x)\to -\frac {3}{7} \sqrt [3]{-1} \sqrt [3]{a} x^{7/3}+c_1 \\ y(x)\to \frac {3}{7} (-1)^{2/3} \sqrt [3]{a} x^{7/3}+c_1 \\ \end{align*}