2.12 problem Differential equations with Linear Coefficients. Exercise 8.12, page 69

Internal problem ID [3944]

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 8.12, page 69.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]

Solve \begin {gather*} \boxed {3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.75 (sec). Leaf size: 46

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

\[ y \relax (x ) = \frac {9}{2}-\frac {\RootOf \left (\left (2 x +4\right )^{5} c_{1} \textit {\_Z}^{25}-5 \left (2 x +4\right )^{5} c_{1} \textit {\_Z}^{20}-2\right )^{5} \left (2 x +4\right )}{4}+\frac {3 x}{2} \]

Solution by Mathematica

Time used: 60.111 (sec). Leaf size: 3081

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

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