4.37.1 \(y''(x)+3 y(x) y'(x)=f(x)+g(x) y(x)-y(x)^3\)
4.37.2 \(y''(x)=(f(x)-3 y(x)) y'(x)+f(x) y(x)^2-y(x)^3\)
4.37.3 \(y''(x)=a \left (2 y(x) y'(x)+1\right )\)
4.37.4 \(a \left (y(x)^2-1\right ) y'(x)+b y(x)+y''(x)=0\)
4.37.5 \(y'(x) f(x,y(x))+g(x,y(x))+y''(x)=0\)
4.37.6 \(y''(x)=\left (x^2-y'(x)\right )^2+2 x\)
4.37.7 \(y''(x)+2 y'(x)^2 \tan (y(x))+2 \cot (x) y'(x)=0\)
4.37.8 \(y''(x)=a y'(x)^2\)
4.37.9 \(y''(x)=a^2+b^2 y'(x)^2\)
4.37.10 \(a y'(x)^2+b y(x)+y''(x)=0\)
4.37.11 \(a y'(x)^2+b \sin (y(x))+y''(x)=0\)
4.37.12 \(a y'(x)^2+b y'(x)+c y(x)+y''(x)=0\)
4.37.13 \(y''(x)=e^x y'(x)^2\)
4.37.14 \(f(x) y'(x)+g(x) y'(x)^2+y''(x)=0\)
4.37.15 \(a y(x) y'(x)^2+b y(x)+y''(x)=0\)
4.37.16 \(f(y(x)) y'(x)^2+g(y(x))+y''(x)=0\)
4.37.17 \(f(x) y'(x)+g(y(x)) y'(x)^2+y''(x)=0\)
4.37.18 \(f(y(x)) y'(x)+g(y(x)) y'(x)^2+y''(x)=0\)
4.37.19 \(f(y(x)) y'(x)+g(y(x)) y'(x)^2+h(y(x))+y''(x)=0\)
4.37.20 \(y''(x)+y'(x)^3+y'(x)=0\)
4.37.21 \(y''(x)=(a-x) y'(x)^3\)
4.37.22 \(y''(x)+\left (e^{2 y(x)}+x\right ) y'(x)^3=0\)
4.37.23 \(y''(x)+4 y'(x)^3+2 y'(x)=0\)
4.37.24 \(a y'(x)^3+y''(x)=0\)
4.37.25 \(y''(x)=x y'(x)^3\)
4.37.26 \(y'(x)^3 (a x+b y(x))+y''(x)=0\)
4.37.27 \(a y(x) \left (y'(x)^2+1\right )^2+y''(x)=0\)
4.37.28 \(y''(x)=a \left (x y'(x)-y(x)\right )^k\)
4.37.29 \(f(x) y'(x)^k+g(x) y'(x)+y''(x)=0\)
4.37.30 \(y''(x)=A x^a y(x)^b y'(x)^c\)
4.37.31 \(y''(x)=a \sqrt {y'(x)^2+1}\)
4.37.32 \(y''(x)=a \sqrt {b y(x)^2+y'(x)^2}\)
4.37.33 \(y''(x)=a \left (y'(x)^2+1\right )^{3/2}\)
4.37.34 \(y''(x)=a x \left (y'(x)^2+1\right )^{3/2}\)
4.37.35 \(y''(x)=a y(x) \left (y'(x)^2+1\right )^{3/2}\)
4.37.36 \(y''(x)=a y(x) \left (\left (b-y'(x)\right )^2+1\right )^{3/2}\)
4.37.37 \(y''(x)=a \left (y'(x)^2+1\right )^{3/2} (b+c x+y(x))\)
4.37.38 \(y''(x)+y(x)^3 y'(x)=y(x) y'(x) \sqrt {4 y'(x)+y(x)^4}\)
4.37.39 \(y''(x)=f\left (y'(x)\right )\)
4.37.40 \(y''(x)=f\left (a x+b y(x),y'(x)\right )\)
4.37.41 \(y''(x)=y(x) f\left (x,\genfrac {}{}{}{}{y'(x)}{y(x)}\right )\)
4.37.42 \(y''(x)=x^{n-2} f\left (x^{-n} y(x),x^{1-n} y'(x)\right )\)
4.37.43 \(2 y''(x)=12 y(x)^2+1\)
4.37.44 \(2 y''(x)=y(x) \left (a-y(x)^2\right )\)
4.37.45 \(8 y''(x)+9 y'(x)^4=0\)
4.37.46 \(a x e^{y(x)}+x y''(x)+y'(x)=0\)
4.37.47 \(x y''(x)+2 y'(x)+x y(x)^5=0\)
4.37.48 \(x y(x)^n+x y''(x)+2 y'(x)=0\)
4.37.49 \(x^m y(x)^n+x y''(x)+2 y'(x)=0\)
4.37.50 \(a x^m y(x)^n+x y''(x)+2 y'(x)=0\)