4.46.1 \(x^2 y''''(x)=2 y''(x)\)
4.46.2 \(x^2 y''''(x)+4 x y'''(x)+2 y''(x)=0\)
4.46.3 \(x^2 y''''(x)+6 x y'''(x)+6 y''(x)=0\)
4.46.4 \(x^2 y''''(x)+8 x y'''(x)+12 y''(x)=0\)
4.46.5 \(x^2 y''''(x)+8 x y'''(x)+a^2 (-y(x))+12 y''(x)=0\)
4.46.6 \((a+x)^2 y''''(x)=1\)
4.46.7 \(32 x (a-b+2) y'''(x)+16 x^2 y''''(x)+16 (a-b+1) (a-b+2) y''(x)+c^4 (-y(x))=0\)
4.46.8 \(x^3 y''''(x)+2 x^2 y'''(x)+a^4 \left (-x^3\right ) y(x)-x y''(x)=0\)
4.46.9 \(x^3 y''''(x)+6 x^2 y'''(x)+6 x y''(x)=0\)
4.46.10 \(x^2 (a+b+c+3) y'''(x)+x^3 y''''(x)+x (a b+a c+a+b c+b+c+1) y''(x)-y'(x) (x-a b c)-k y(x)=0\)
4.46.11 \(x^4 y''''(x)+6 x^3 y'''(x)+4 x^2 y''(x)-2 x y'(x)-4 y(x)=0\)
4.46.12 \(x^4 y''''(x)+6 x^3 y'''(x)+9 x^2 y''(x)+3 x y'(x)+y(x)=0\)
4.46.13 \(x^4 y''''(x)+8 x^3 y'''(x)+12 x^2 y''(x)=0\)
4.46.14 \(x^4 y''''(x)+8 x^3 y'''(x)+a y(x)+12 x^2 y''(x)=0\)
4.46.15 \(\text {A1} x^3 y'''(x)+x^4 y''''(x)+\text {A2} x^2 y''(x)+\text {A3} x y'(x)+\text {A4} y(x)=0\)
4.46.16 \(16 a^4 x^4 y''''(x)-32 (1-2 a) a^2 x^3 y'''(x)+16 (1-2 a) (1-a) a^2 x^2 y''(x)-b^4 x^{2/a} y(x)=0\)
4.46.17 \(4 \left (e^x+2\right ) y'''(x)+\left (2 x+e^x\right ) y''''(x)+6 e^x y''(x)+4 e^x y'(x)+e^x y(x)=0\)
4.46.18 \(-y'''(x)+y'''''(x)-2 y''(x)+2 y'(x)=0\)
4.46.19 \(2 y'''(x)+y'''''(x)+y'(x)=0\)
4.46.20 \(2 y'''(x)+y'''''(x)+y'(x)=a x+b \cos (x)+c \sin (x)\)
4.46.21 \(y''''''(x)=0\)
4.46.22 \(y''''''(x)+a y(x)=0\)
4.46.23 \(2 y'''(x)+y''''''(x)+y(x)=0\)
4.46.24 \(y''''''''(x)=y(x)\)
4.46.25 \(y''''''''(x)-2 y''''+y(x)=0\)
4.46.26 \(\genfrac {}{}{}{}{\partial ^{2 n}y(x)}{\partial x^{2 n}}=a^{2 n} y(x)\)
4.46.27 \(x^n \genfrac {}{}{}{}{\partial ^{2 n}y(x)}{\partial x^{2 n}}=y(x)\)
4.46.28 \(x^{n+\genfrac {}{}{}{}{1}{2}} \genfrac {}{}{}{}{\partial ^{2 n+1}y(x)}{\partial x^{2 n+1}}=y(x)\)
4.46.29 \(y^{(n)}(x)=e^x x\)
4.46.30 \(a m x^{m-1} y(x)+a x^m y'(x)+y^{(n)}(x)=0\)
4.46.31 \((a-x)^n (b-x)^n y^{(n)}(x)=c y(x)\)
4.46.32 \(y'''(x)=y'(x) \left (y'(x)+1\right )\)
4.46.33 \(y'''(x)+y'(x)^2-y(x) y'(x)=0\)
4.46.34 \(y'''(x)+a y(x) y''(x)=0\)
4.46.35 \(x^2 y'''(x)+x y''(x)-(1-2 x y(x)) y'(x)+y(x)^2=f(x)\)
4.46.36 \(x^2 y'''(x)-x (1-y(x)) y''(x)+x y'(x)^2+(1-y(x)) y'(x)=0\)
4.46.37 \(y(x) y'''(x)+y(x)^3 y'(x)-y'(x) y''(x)=0\)
4.46.38 \((a+y(x)) y'''(x)+3 y'(x) y''(x)=0\)
4.46.39 \(x^3 y(x) y'''(x)+3 x^3 y'(x) y''(x)+9 x^2 y(x) y''(x)+9 x^2 y'(x)^2+18 x y(x) y'(x)+3 y(x)^2=0\)
4.46.40 \(\left (y(x)^2+x\right ) y'''(x)+3 y''(x)+2 y'(x)^3+6 y(x) y'(x) y''(x)=0\)
4.46.41 \(4 y(x)^2 y'''(x)+15 y'(x)^3-18 y(x) y'(x) y''(x)=0\)
4.46.42 \(9 y(x)^2 y'''(x)+40 y'(x)^3-45 y(x) y'(x) y''(x)=0\)
4.46.43 \(y'(x) y'''(x)+y'(x)^2=2 y''(x)^2\)
4.46.44 \(y'(x) y''(x)=a x y'(x)^5+3 y''(x)^2\)
4.46.45 \(2 y'(x) y'''(x)=2 y''(x)^2\)
4.46.46 \(\left (y'(x)^2+1\right ) y'''(x)=3 y'(x) y''(x)^2\)
4.46.47 \(\left (y'(x)^2+1\right ) y'''(x)=y''(x)^2 \left (a+3 y'(x)\right )\)
4.46.48 \(y'(x)^3 y'''(x)=1\)
4.46.49 \(y''(x) y'''(x)=2\)
4.46.50 \(y''(x) y'''(x)=a \sqrt {b^2 y''(x)^2+1}\)