64.4.19 problem 19

Internal problem ID [13308]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 05:17:36 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x -5 y+\left (4 x -y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.306 (sec). Leaf size: 35

dsolve([(2*x-5*y(x))+(4*x-y(x))*diff(y(x),x)=0,y(1) = 4],y(x), singsol=all)
 

\begin{align*} y &= 6-2 x -6 \sqrt {1-x} \\ y &= 6-2 x +6 \sqrt {1-x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 62

DSolve[{(2*x-5*y[x])+(4*x-y[x])*D[y[x],x]==0,{y[1]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]-4}{(K[1]-1) (K[1]+2)}dK[1]=\int _1^4\frac {K[1]-4}{(K[1]-1) (K[1]+2)}dK[1]-\log (x),y(x)\right ] \]