12.5.20 problem 17

Internal problem ID [1644]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 17
Date solved : Monday, January 27, 2025 at 05:15:43 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 56

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

\begin{align*} y &= \left (4 \ln \left (x \right )+c_1 \right )^{{1}/{4}} x \\ y &= -\left (4 \ln \left (x \right )+c_1 \right )^{{1}/{4}} x \\ y &= -i \left (4 \ln \left (x \right )+c_1 \right )^{{1}/{4}} x \\ y &= i \left (4 \ln \left (x \right )+c_1 \right )^{{1}/{4}} x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.175 (sec). Leaf size: 76

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

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