64.3.10 problem 11

Internal problem ID [13281]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page 37
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 05:14:22 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

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

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

\[ y = -\frac {x^{2}}{4}+\frac {\sqrt {x^{4}+24 x +56}}{4} \]

✓ Solution by Mathematica

Time used: 0.147 (sec). Leaf size: 27

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

\[ y(x)\to \frac {1}{4} \left (\sqrt {x^4+24 x+56}-x^2\right ) \]