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4.38
Problems 1851 to 1900
4.38.1
\(a y'(x)+b x e^{y(x)}+x y''(x)=0\)
4.38.2
\(\left (2-a x^2\right ) y'(x)+x y''(x)=0\)
4.38.3
\(x y''(x)=(1-y(x)) y'(x)\)
4.38.4
\(x y''(x)+x y'(x)^2=y'(x)\)
4.38.5
\(x y''(x)=x y'(x)^2+y'(x)\)
4.38.6
\(x y''(x)+2 x y'(x)^2-2 y'(x)=0\)
4.38.7
\(x y''(x)=x^2 y'(x)^2-2 y'(x)-y(x)^2\)
4.38.8
\(a x^2 y'(x)^2+x y''(x)+2 y'(x)=b\)
4.38.9
\(\left (a x y'(x)-y(x)\right )^2+x y''(x)=b\)
4.38.10
\(x y''(x)=y'(x)^3+y'(x)\)
4.38.11
\(x y''(x)+2 y'(x)=a x^{2 k} y'(x)^k\)
4.38.12
\(2 x y''(x)+y'(x)^3+y'(x)=0\)
4.38.13
\(a y(x) \left (1-y(x)^n\right )+x^2 y''(x)=0\)
4.38.14
\(a e^{y(x)-1}+x^2 y''(x)=0\)
4.38.15
\((a+1) x y'(x)+x^2 y''(x)=x^k f\left (x^k y(x),k y(x)+x y'(x)\right )\)
4.38.16
\(x^2 y''(x)+y'(x)^2=0\)
4.38.17
\(x^2 y''(x)=\left (3 x-2 y'(x)\right ) y'(x)\)
4.38.18
\(x^2 y''(x)+x^2 y'(x)^2+4 x y'(x)+2=0\)
4.38.19
\(x^2 y''(x)=x^4 y'(x)^2-4 x^2 y(x)^2+6 y(x)\)
4.38.20
\(a \left (x y'(x)-y(x)\right )^2+x^2 y''(x)=b x^2\)
4.38.21
\(a x^4 y'(x)^2+x^2 y''(x)+2 x y(x)=b\)
4.38.22
\(a y(x) y'(x)^2+b x+x^2 y''(x)=0\)
4.38.23
\(x^2 y''(x)=\sqrt {a x^2 y'(x)^2+b y(x)^2}\)
4.38.24
\(x^2 y''(x)=y(x) f\left (\genfrac {}{}{}{}{x y'(x)}{y(x)}\right )\)
4.38.25
\(\left (x^2+1\right ) y''(x)+y'(x)^2+1=0\)
4.38.26
\(a y(x)^3+9 x^2 y''(x)+2 y(x)=0\)
4.38.27
\(x^3 y''(x)-x^2 y'(x)=3-x^2\)
4.38.28
\(x^3 \left (y''(x)+y(x) y'(x)-y(x)^3\right )+12 x y(x)+24=0\)
4.38.29
\(x^3 y''(x)=a \left (x y'(x)-y(x)\right )^2\)
4.38.30
\(2 x^3 y''(x)+x^2 (2 x y(x)+9) y'(x)+x y(x) \left (-2 x^2 y(x)^2+3 x y(x)+12\right )-6=0\)
4.38.31
\(x^4 y''(x)=x \left (x^2+2 y(x)\right ) y'(x)-4 y(x)^2\)
4.38.32
\(x^4 y''(x)=x^2 y'(x) \left (y'(x)+x\right )-4 y(x)^2\)
4.38.33
\(x^4 y''(x)+\left (x y'(x)-y(x)\right )^3=0\)
4.38.34
\(x^a y''(x)+y(x)^b=0\)
4.38.35
\(\left (1-12 x^2\right ) \left (3 y'(x)+y(x)^2\right )+2 x \left (1-4 x^2\right ) \left (y''(x)+y(x) y'(x)-y(x)^3\right )-48 x y(x)+24=0\)
4.38.36
\(a x y(x)+b-\left (k x^{k-1}-12 x^2\right ) \left (3 y'(x)+y(x)^2\right )+2 \left (x^k-4 x^3\right ) \left (y''(x)+y(x) y'(x)-y(x)^3\right )=0\)
4.38.37
\(\sqrt {x} y''(x)=y(x)^{3/2}\)
4.38.38
\(x^{3/2} y''(x)=f\left (\genfrac {}{}{}{}{y(x)}{\sqrt {x}}\right )\)
4.38.39
\(y''(x) \left (a+2 b x+c x^2\right )^{3/2}=f\left (\genfrac {}{}{}{}{x}{\sqrt {a+2 b x+c x^2}}\right )\)
4.38.40
\(f(x) f'(x) y'(x)+f(x)^2 y''(x)=g\left (y(x),f(x) y'(x)\right )\)
4.38.41
\(f(x)^2 y''(x)=y'(x) \left (3 f(x) f'(x)-f(x)^2 y(x)+3 f(x)^3\right )-24 f(x)^4\)
4.38.42
\(f(x)^2 y''(x)=-a f(x)^5+3 f(x) f'(x)-f(x)^2 y(x)+3 f(x)^3\)
4.38.43
\(2 f(x)^2 y''(x)=f(x) y'(x) \left (3 f'(x)-2 f(x) y(x)\right )+f(x) y(x)^2 f'(x)+y(x) \left (f(x) f''(x)-2 f'(x)^2-2 f(x)^3\right )+2 f(x)^2 y(x)^3\)
4.38.44
\(y(x) y''(x)=a\)
4.38.45
\(y(x) y''(x)=y'(x)^2\)
4.38.46
\(y(x) y''(x)+y'(x)^2=0\)
4.38.47
\(y(x) y''(x)=y'(x)^2-a^2\)
4.38.48
\(y(x) y''(x)+y'(x)^2=a^2\)
4.38.49
\(y(x) y''(x)+y'(x)^2+y(x)^2=0\)
4.38.50
\(2 a^2 y(x)^2+y(x) y''(x)+y'(x)^2=0\)
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