- Bernoulli Equations 1 (46.76 KiB) Viewed 65 times
- Bernoulli Equations 2 (23.85 KiB) Viewed 65 times
6.39. y + xy=6x√y 64 y 6.53. y + ²y=-x²y³; y(-1) = 2 6.42. y' + y = y²ex Excercies: Bernoulli Equations
Bernoulli Equations
-
answerhappygod
- Site Admin
- Posts: 899603
- Joined: Mon Aug 02, 2021 8:13 am
Bernoulli Equations
Bernoulli Equations
Bernoulli Equations A Bernoulli differential equation has the form y' + p(x)y= q (x)y" Where n is a real number. The substitution z = y¹-n, z' = (1-n)y "y' Transforms (1) into a linear differential equation in the unknown function z(x). y-"y' + p(x)yy" = q (x)y"y" z' 1-n z' + (1-n)p(x)z = (1-n)q(x) + p(x)z = q (x) z = y¹-n = e-f(1-n)p(x) dx (1) Jeft-m el(1-n)p(x) dx (1-n)q(x) dx + C *
6.39. y + xy=6x√y 64 y 6.53. y + ²y=-x²y³; y(-1) = 2 6.42. y' + y = y²ex Excercies: Bernoulli Equations
Bernoulli Equations A Bernoulli differential equation has the form y' + p(x)y= q (x)y" Where n is a real number. The substitution z = y¹-n, z' = (1-n)y "y' Transforms (1) into a linear differential equation in the unknown function z(x). y-"y' + p(x)yy" = q (x)y"y" z' 1-n z' + (1-n)p(x)z = (1-n)q(x) + p(x)z = q (x) z = y¹-n = e-f(1-n)p(x) dx (1) Jeft-m el(1-n)p(x) dx (1-n)q(x) dx + C *
6.39. y + xy=6x√y 64 y 6.53. y + ²y=-x²y³; y(-1) = 2 6.42. y' + y = y²ex Excercies: Bernoulli Equations