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How to solve $y^{\prime\prime}=y^2-y, y^{\prime}=0$ when $y(x_0)=1, y^{\prime}(x_0)=2$ where $x_0=\sqrt{2}$

score 2.6k · Answer 1 · 2026-03-25 00:41:24

2.6k

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How to solve $y^{\prime\prime}=y^2-y, y^{\prime}=0$ when $y(x_0)=1, y^{\prime}(x_0)=2$ where $x_0=\sqrt{2}$

Published on 25 Mar 2026 - 0:41

score 667 · Answer 2 · 2026-03-25 03:04:12

667

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Symmetric polynomial identities: $(x,y,z)^n$ in terms of $\sigma _1=x+y+z$, $\sigma _2 = xy+yz+xz$ and $\sigma _3 = xyz$

Published on 25 Mar 2026 - 3:04

score 136 · Answer 3 · 2018-08-11 11:05:29

136

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Substitution leads me to wrong result for the integral $\int_0^x\lambda e^{-\lambda x}dx$

Published on 11 Aug 2018 - 11:05

score 114 · Answer 4 · 2026-03-25 12:52:37

114

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Inequality about Schur

Published on 25 Mar 2026 - 12:52

score 127 · Answer 5 · 2018-08-13 21:10:45

127

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$u$-substitution failure in finding $f'(x)$ where $ f(x) = \int_x^0 \frac{\cos(xt)}{t}\, dt$

Published on 13 Aug 2018 - 21:10

score 87 · Answer 6 · 2018-08-13 23:10:13

87

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Is success realistic using u-substitution when the derivative isn't in the integrand?

Published on 13 Aug 2018 - 23:10

score 149 · Answer 7 · 2018-08-14 12:59:27

149

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For positive number $a,b$, when $a,b$ satisfies $2a^2 +7ab+3b^2=7$, what is maximum value of $a+{\sqrt{3ab}}+2b$

Published on 14 Aug 2018 - 12:59

score 68 · Answer 8 · 2018-08-15 14:41:01

68

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Can anyone evaluate this definite integral?

Published on 15 Aug 2018 - 14:41

score 224 · Answer 9 · 2018-08-17 11:31:59

224

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Help evaluating $ \int \frac {\sqrt{x^2-1}}x \ dx$

Published on 17 Aug 2018 - 11:31

score 285 · Answer 10 · 2018-08-18 10:41:55

285

Views

Second order linear differential equation with non-constants coefficients $xy''+2(x+1)y'+((x+2)y=0$

Published on 18 Aug 2018 - 10:41

score 296 · Answer 11 · 2018-08-18 20:44:53

296

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Using Substitution to Solve a 1st Order Differential Equation

Published on 18 Aug 2018 - 20:44

score 1.6k · Answer 12 · 2018-08-18 21:16:14

1.6k

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Solve $y^2y'= y^3-3x$ for $y(0)=2$

Published on 18 Aug 2018 - 21:16

score 172 · Answer 13 · 2026-03-25 07:53:19

172

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Solve $8\sin x=\frac{\sqrt{3}}{\cos x}+\frac{1}{\sin x}$

Published on 25 Mar 2026 - 7:53

score 226 · Answer 14 · 2026-03-25 06:06:40

226

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If $x+y+z=3$ then $\sum x\sqrt{x^3+3y} \ge 6$

Published on 25 Mar 2026 - 6:06

score 206 · Answer 15 · 2026-03-25 04:39:21

206

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Mellin transform - change of variables in double integral

Published on 25 Mar 2026 - 4:39

List Question

How to solve $y^{\prime\prime}=y^2-y, y^{\prime}=0$ when $y(x_0)=1, y^{\prime}(x_0)=2$ where $x_0=\sqrt{2}$

Symmetric polynomial identities: $(x,y,z)^n$ in terms of $\sigma _1=x+y+z$, $\sigma _2 = xy+yz+xz$ and $\sigma _3 = xyz$

Substitution leads me to wrong result for the integral $\int_0^x\lambda e^{-\lambda x}dx$

Inequality about Schur

$u$-substitution failure in finding $f'(x)$ where $ f(x) = \int_x^0 \frac{\cos(xt)}{t}\, dt$

Is success realistic using u-substitution when the derivative isn't in the integrand?

For positive number $a,b$, when $a,b$ satisfies $2a^2 +7ab+3b^2=7$, what is maximum value of $a+{\sqrt{3ab}}+2b$

Can anyone evaluate this definite integral?

Help evaluating $ \int \frac {\sqrt{x^2-1}}x \ dx$

Second order linear differential equation with non-constants coefficients $xy''+2(x+1)y'+((x+2)y=0$

Using Substitution to Solve a 1st Order Differential Equation

Solve $y^2y'= y^3-3x$ for $y(0)=2$

Solve $8\sin x=\frac{\sqrt{3}}{\cos x}+\frac{1}{\sin x}$

If $x+y+z=3$ then $\sum x\sqrt{x^3+3y} \ge 6$

Mellin transform - change of variables in double integral

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