78.1.11 problem 1 (L)

Internal problem ID [18066]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 1 (L)
Date solved : Tuesday, January 28, 2025 at 11:24:40 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.103 (sec). Leaf size: 77

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

\begin{align*} y &= -\frac {1}{4 x^{2}} \\ y &= \frac {-i c_{1} -x}{c_{1}^{2} x} \\ y &= \frac {i c_{1} -x}{x \,c_{1}^{2}} \\ y &= \frac {i c_{1} -x}{x \,c_{1}^{2}} \\ y &= \frac {-i c_{1} -x}{c_{1}^{2} x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.549 (sec). Leaf size: 123

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

\begin{align*} \text {Solve}\left [-\frac {x \sqrt {4 x^2 y(x)+1} \text {arctanh}\left (\sqrt {4 x^2 y(x)+1}\right )}{\sqrt {4 x^4 y(x)+x^2}}-\frac {1}{2} \log (y(x))&=c_1,y(x)\right ] \\ \text {Solve}\left [\frac {x \sqrt {4 x^2 y(x)+1} \text {arctanh}\left (\sqrt {4 x^2 y(x)+1}\right )}{\sqrt {4 x^4 y(x)+x^2}}-\frac {1}{2} \log (y(x))&=c_1,y(x)\right ] \\ y(x)\to 0 \\ \end{align*}