Question Details
A bernoulli differential equation is one of the form dy/dx +P(x)y=Q(x)y^n (*)
Observe that if n=0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=y^1-n transforms the Bernoulli equation into the linear equation du/dx + (1-n)P(x)u=(1-n)Q(x)
Solve the equation using an appropriate substitution to solve the equation
xy’ +y=-3xy^2 and y(1)=2
I can't seem to solve (B) and (D)
a) The differential ewuation can be written in the form (*) with P(x)____?, Q(x)_____? And n=?
Answer: P(x)=1/x , Q(x)=-3, n=2
b) The substitution u=__y^-1_____ will transform it into the linear equation
du/dx+ _?____u= ?
Answer:du/dx+ _?____u= -3
c) Using the substitution in part(b), we rewrite the initial condition in terms of X and u: u(1)
A bernoulli differential equation is one of the form dy/dx +P(x)y=Q(x)y^n (*)
Observe that if n=0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=y^1-n transforms the Bernoulli equation into the linear equation du/dx + (1-n)P(x)u=(1-n)Q(x)
Solve the equation using an appropriate substitution to solve the equation
xy’ +y=-3xy^2 and y(1)=2
I can't seem to solve (B) and (D)
a) The differential ewuation can be written in the form (*) with P(x)____?, Q(x)_____? And n=?
Answer: P(x)=1/x , Q(x)=-3, n=2
b) The substitution u=__y^-1_____ will transform it into the linear equation
du/dx+ _?____u= ?
Answer:du/dx+ _?____u= -3
c) Using the substitution in part(b), we rewrite the initial condition in terms of X and u: u(1)
1
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