12.6.23 problem 23

Internal problem ID [1702]
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 : 23
Date solved : Monday, January 27, 2025 at 05:30:57 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 7 x +4 y+\left (4 x +3 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.029 (sec). Leaf size: 53

dsolve((7*x+4*y(x))+(4*x+3*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {-4 c_1 x -\sqrt {-5 c_1^{2} x^{2}+3}}{3 c_1} \\ y &= \frac {-4 c_1 x +\sqrt {-5 c_1^{2} x^{2}+3}}{3 c_1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.438 (sec). Leaf size: 118

DSolve[(7*x+4*y[x])+(4*x+3*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{3} \left (-4 x-\sqrt {-5 x^2+3 e^{2 c_1}}\right ) \\ y(x)\to \frac {1}{3} \left (-4 x+\sqrt {-5 x^2+3 e^{2 c_1}}\right ) \\ y(x)\to \frac {1}{3} \left (-\sqrt {5} \sqrt {-x^2}-4 x\right ) \\ y(x)\to \frac {1}{3} \left (\sqrt {5} \sqrt {-x^2}-4 x\right ) \\ \end{align*}