Internal problem ID [5085]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.2 FIRST ORDER ODE. Page
114
Problem number: Example 3.5.
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 {y^{\prime }-\frac {x +y-1}{-y+3+x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 31
dsolve(diff(y(x),x)=(x+y(x)-1)/(x-y(x)+3),y(x), singsol=all)
\[ y \relax (x ) = 2-\tan \left (\RootOf \left (2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \left (x +1\right )+2 c_{1}\right )\right ) \left (x +1\right ) \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 59
DSolve[y'[x]==(x+y[x]-1)/(x-y[x]+3),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \text {ArcTan}\left (1-\frac {2 (x+1)}{-y(x)+x+3}\right )+\log \left (\frac {x^2+y(x)^2-4 y(x)+2 x+5}{2 (x+1)^2}\right )+2 \log (x+1)+c_1=0,y(x)\right ] \]