32.2.10 problem Differential equations with Linear Coefficients. Exercise 8.10, page 69

Internal problem ID [5794]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 8
Problem number : Differential equations with Linear Coefficients. Exercise 8.10, page 69
Date solved : Monday, January 27, 2025 at 01:18:15 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.913 (sec). Leaf size: 33

dsolve((3*x-2*y(x)+4)-(2*x+7*y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-\sqrt {7+15625 \left (x +\frac {26}{25}\right )^{2} c_{1}^{2}}+\left (-50 x +25\right ) c_{1}}{175 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.140 (sec). Leaf size: 65

DSolve[(3*x-2*y[x]+4)-(2*x+7*y[x]-1)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{7} \left (-\sqrt {25 x^2+52 x+1+49 c_1}-2 x+1\right ) \\ y(x)\to \frac {1}{7} \left (\sqrt {25 x^2+52 x+1+49 c_1}-2 x+1\right ) \\ \end{align*}