82.3.4 problem Ex. 4

Internal problem ID [18734]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 16
Problem number : Ex. 4
Date solved : Tuesday, January 28, 2025 at 12:13:27 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.155 (sec). Leaf size: 55

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

\[ -\frac {\ln \left (\frac {-x^{2}+2 x y \left (x \right )+2 y \left (x \right )^{2}}{x^{2}}\right )}{2}+\frac {\sqrt {3}\, \operatorname {arctanh}\left (\frac {\left (2 y \left (x \right )+x \right ) \sqrt {3}}{3 x}\right )}{6}-\ln \left (x \right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 63

DSolve[(4*y[x]+3*x)*D[y[x],x]+y[x]-2*x==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {1}{6} \left (\left (6+\sqrt {3}\right ) \log \left (-\frac {2 y(x)}{x}+\sqrt {3}-1\right )-\left (\sqrt {3}-6\right ) \log \left (\frac {2 y(x)}{x}+\sqrt {3}+1\right )\right )=-2 \log (x)+c_1,y(x)\right ] \]