29.17.13 problem 472

Internal problem ID [5070]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 472
Date solved : Monday, January 27, 2025 at 10:07:37 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y&=0 \end{align*}

✓ Solution by Maple

Time used: 3.534 (sec). Leaf size: 31

dsolve((19+9*x+2*y(x))*diff(y(x),x)+18-2*x-6*y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-\sqrt {1+\left (-40 x -120\right ) c_{1}}-1+\left (4 x +44\right ) c_{1}}{8 c_{1}} \]

✓ Solution by Mathematica

Time used: 14.727 (sec). Leaf size: 276

DSolve[(19+9 x+2 y[x])D[y[x],x]+18-2 x-6 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{\frac {i \sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )-i}}+(1-i)}-\frac {19}{2} \\ y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{(1-i)-\frac {i \sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )-i}}}-\frac {19}{2} \\ y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{(1-i)-\frac {\sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )+i}}}-\frac {19}{2} \\ y(x)\to -\frac {9 x}{2}+\frac {(5-5 i) (x+3)}{\frac {\sqrt {2}}{\sqrt {(x+3) \cosh \left (\frac {2 c_1}{9}\right )+(x+3) \sinh \left (\frac {2 c_1}{9}\right )+i}}+(1-i)}-\frac {19}{2} \\ y(x)\to -2 (x+1) \\ y(x)\to \frac {x+11}{2} \\ \end{align*}