5. Find the general solution of the Bernoulli equation CO dy - y = e2xy3
1: The equation dy + 2y = xy-2 is an example of a Bernoulli equation. (a) Show that the substitution v = y; reduces eqauation to do + 6u = 3x. (b) Find the general solution to the equation in part(a).
Use the method for solving Bernoulli equations to solve the following differential equation, dy Y = 2x8y² dy Ignoring lost solutions, if any, the general solution is y (Type an expression using x as the variable.)
dy 2. Find the general solution of -y+e"y dv -6xy 3. Find the general solution of t dr 4y+9x2 dy dx Find the general solution of бх2e" + 4y. 4. 5. Find the general solution of dr (y +2) dy 5x +4y Find the general solution of dx 8y3 d By'-4x
question2
Find the of the equation general solution dy - 4x3y²-3x²y dy x22xHy
5. Given the differential equation: dy 1 +-y = 3x2 dx Find (a) (b) the general solution for the differential equation; and (6 marks) the particular solution for the differential equation if the boundary condition is y(1) =2. (2 marks)
Find a general solution to the given Cauchy-Euler equation for t> 0. 2d²y dy +41 - 10y = 0 dt at² The general solution is y(t) =
(15 points) A Bernoulli differential equation is one of the form dy dar + P(x)y= Q(x)y". Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=yl-n transforms the Bernoulli equation into the linear equation du + (1 - n)P(x) = (1 - nQ(x). dx Use an appropriate substitution to solve the equation xy' +y=2xy? and find the solution that satisfies y(1) = 1.
Find the general solution for dy/dx = (x+y+5)^2
Find a general solution to the given Cauchy-Euler equation for t> 0. 12d²y dy + 2t- dt - 6y = 0 dt² The general solution is y(t) =
Find the general solution of the differential equation: dy/dt=(-y/t)+6. Use lower case c for constant in answer. y(t)=