29.18.10 problem 486

Internal problem ID [5084]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 486
Date solved : Monday, January 27, 2025 at 10:08:34 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (5+3 x -4 y\right ) y^{\prime }&=2+7 x -3 y \end{align*}

✓ Solution by Maple

Time used: 0.712 (sec). Leaf size: 33

dsolve((5+3*x-4*y(x))*diff(y(x),x) = 2+7*x-3*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-\sqrt {4-6859 \left (x -\frac {7}{19}\right )^{2} c_{1}^{2}}+\left (57 x +95\right ) c_{1}}{76 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.134 (sec). Leaf size: 71

DSolve[(5+3 x-4 y[x])D[y[x],x]==2+7 x-3 y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{4} \left (-i \sqrt {19 x^2-14 x-25-16 c_1}+3 x+5\right ) \\ y(x)\to \frac {1}{4} \left (i \sqrt {19 x^2-14 x-25-16 c_1}+3 x+5\right ) \\ \end{align*}