28.1.74 problem 77

Internal problem ID [4380]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 77
Date solved : Monday, January 27, 2025 at 09:09:39 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} 2 x^{3}-y^{4}+x y^{3} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 63

dsolve((2*x^3-y(x)^4)+(x*y(x)^3)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.306 (sec). Leaf size: 88

DSolve[(2*x^3-y[x]^4)+(x*y[x]^3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x^{3/4} \sqrt [4]{8+c_1 x} \\ y(x)\to -i x^{3/4} \sqrt [4]{8+c_1 x} \\ y(x)\to i x^{3/4} \sqrt [4]{8+c_1 x} \\ y(x)\to x^{3/4} \sqrt [4]{8+c_1 x} \\ \end{align*}