60.1.226 problem 227

Internal problem ID [10240]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 227
Date solved : Monday, January 27, 2025 at 06:40:59 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2&=0 \end{align*}

✓ Solution by Maple

Time used: 0.418 (sec). Leaf size: 33

dsolve((4*y(x)-3*x-5)*diff(y(x),x)-3*y(x)+7*x+2=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 71

DSolve[(4*y[x]-3*x-5)*D[y[x],x]-3*y[x]+7*x+2==0,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*}