12.6.18 problem 18

Internal problem ID [1697]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 18
Date solved : Monday, January 27, 2025 at 05:30:39 AM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 22

dsolve([(4*x^3*y(x)^2-6*x^2*y(x)-2*x-3)+(2*x^4*y(x)-2*x^3)*diff(y(x),x)=0,y(1) = 3],y(x), singsol=all)
 

\[ y = \frac {x +\sqrt {2 x^{2}+3 x -1}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.785 (sec). Leaf size: 31

DSolve[{(4*x^3*y[x]^2-6*x^2*y[x]-2*x-3)+(2*x^4*y[x]-2*x^3)*D[y[x],x]==0,y[1]==3},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^3+\sqrt {x^4 \left (2 x^2+3 x-1\right )}}{x^4} \]