20.2.7 problem Problem 7

Internal problem ID [3599]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.4, Separable Differential Equations. page 43
Problem number : Problem 7
Date solved : Monday, January 27, 2025 at 07:47:08 AM
CAS classification : [_separable]

\begin{align*} y-x y^{\prime }&=3-2 x^{2} y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(y(x)-x*diff(y(x),x)=3-2*x^2*diff(y(x),x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{1} x -3}{2 x -1} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 24

DSolve[y[x]-x*D[y[x],x]==3-2*x^2*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {3+c_1 x}{1-2 x} \\ y(x)\to 3 \\ \end{align*}