7.5.22 problem 22

Internal problem ID [126]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 22
Date solved : Friday, February 07, 2025 at 07:53:22 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y^{\prime } x^{2}+2 x y&=5 y^{4} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 109

dsolve(x^2*diff(y(x),x)+2*x*y(x)=5*y(x)^4,y(x), singsol=all)
 

\begin{align*} y &= \frac {7^{{1}/{3}} {\left (x \left (7 c_1 \,x^{7}+15\right )^{2}\right )}^{{1}/{3}}}{7 c_1 \,x^{7}+15} \\ y &= -\frac {7^{{1}/{3}} {\left (x \left (7 c_1 \,x^{7}+15\right )^{2}\right )}^{{1}/{3}} \left (1+i \sqrt {3}\right )}{14 c_1 \,x^{7}+30} \\ y &= \frac {7^{{1}/{3}} {\left (x \left (7 c_1 \,x^{7}+15\right )^{2}\right )}^{{1}/{3}} \left (i \sqrt {3}-1\right )}{14 c_1 \,x^{7}+30} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.797 (sec). Leaf size: 96

DSolve[x^2*D[y[x],x]+2*x*y[x]==5*y[x]^4,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt [3]{-7} \sqrt [3]{x}}{\sqrt [3]{15+7 c_1 x^7}} \\ y(x)\to \frac {\sqrt [3]{7} \sqrt [3]{x}}{\sqrt [3]{15+7 c_1 x^7}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{7} \sqrt [3]{x}}{\sqrt [3]{15+7 c_1 x^7}} \\ y(x)\to 0 \\ \end{align*}