Question

dy/dx = 2 sqrt(y/x) + y/x (x<0)

Find general solution of the given ODE

Answer #1

Find the general solution of the given differential equation
(x+!) dy/dx + (x+2)y = 2xe^-x
y = ______
Determine whether there are any transient terms in the general
solution.

Find the general solution to the ODE y2
-10y+21=dy/dx

1. Consider the ODE dy/ dx = tanh(x) − y tanh(x). Use the
integrating factor method to find the general solution of the ODE.
Find the general solution of the ODE using a different method. Do
you get the same answer? Explain briefly.

Find the general solution and initial value solution: (cos x)dy
= -2y2(tan x)dx, y(0)=1/6

1.Solve the following initial value problem
a) dy/dx= y2/(x-3), with y(4)=2
b) (sqrt(x)) dy/dx = ey+sqrt(x), with y(0)= 0
2. Find an expression for nth term of the
sequence
a) {-1, 13/24, -20/120, 27/720, ...}
b) {4/10, 12/7, 36/4, 108, ...}

find the general solution to the ODE: y''+yx^2 =0

Find a general solution: (dy/dx) = (x+xy^2)/2y

(61). (Bernoulli’s Equation): Find the general solution of the
following first-order differential equations:(a) x(dy/dx)+y=
y^2+ln(x) (b) (1/y^2)(dy/dx)+(1/xy)=1

Solve: 1.dy/dx=(e^(y-x)).secy.(1+x^2),y(0)=0.
2.dy/dx=(1-x-y)/(x+y),y(0)=2 .

Find the general solution of the ODE:
x2(y′)2 + yy′(2x+y) + y2= 0

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