Question

(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

Answer #1

please check the first question it may be wrong second question is Bernoulli I solved that

1. Find the general solution of the first order linear
differential equation: 2*x*dy/dx -y-3/sqrt(x)=0. sqrt() = square
root of ().
2. Are there any transient terms in the general solution?
Justify your answer.

Find general solution to the equations:
1)y'=x-1-y²+xy²
2)xy²dy=(x³+y³)dx

3. Find the general solution to the differential equation:
(x^2 + 1/( x + y) + y cos(xy)) dx + (y ^2 + 1 / (x + y) + x
cos(xy)) dy = 0

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 solution of the first order differential equation
(e^x+y + ye^y)dx +(xe^y - 1)dy =0 with initial value y(0)= -1

Use the method for solving homogeneous equations to solve the
following differential equation.
(9x^2-y^2)dx+(xy-x^3y^-1)dy=0
solution is F(x,y)=C, Where C= ?

Find a particular solution to each of the following differential
equations with the given initial condition:
A) dy/dx=ysinx/1+y^2, y(0)=1
B)dy/dx=xy ln x, y(1)=3
C)xy(1+x^2) dy/dx=(1+y^2), y(1)=0

Homogeneous Differential Equations:
dy/dx = xy/x^(2) - y^(2)
dy/dx = x^2 + y^2 / 2xy

(a) State the interval on which the solution to the differential
equation (x^2-1)dy/dx + ln(x+1)y = 4e^x
with initial condition y(2) = 4 exists. Do not attempt to solve the
equation.
ODE
SHOW ALL STEPS PLEASE.

Solve the following differential equations.
a.) dy/dx+2xy=x, y(0)=2
b.) ?^2(dy/dx)−?y=−y^2

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