50.1.11 problem 1(L)

Internal problem ID [7783]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 1(L)
Date solved : Monday, January 27, 2025 at 03:22:50 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.038 (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 {-c_{1} i-x}{x \,c_{1}^{2}} \\ y &= \frac {c_{1} i-x}{x \,c_{1}^{2}} \\ y &= \frac {c_{1} i-x}{x \,c_{1}^{2}} \\ y &= \frac {-c_{1} i-x}{x \,c_{1}^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.541 (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*}