78.8.26 problem 26

Internal problem ID [18224]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 26
Date solved : Tuesday, January 28, 2025 at 11:40:43 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{2} y^{4}+x^{6}-x^{3} y^{3} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

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

dsolve((x^2*y(x)^4+x^6)-(x^3*y(x)^3)*diff(y(x),x)=0,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: 0.179 (sec). Leaf size: 76

DSolve[(x^2*y[x]^4+x^6)-(x^3*y[x]^3)*D[y[x],x]==0,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*}