Question
In: Math
Determine if exact equation, then solve: x(y+2)y' = lnx+1 , y(1) = -1
Determine if exact equation, then solve:
x(y+2)y' = lnx+1 , y(1) = -1
Solutions
milcah answered 2 years agoRelated Solutions
Determine whether the given differential equation is exact. If it is exact, solve it. i) (x...
Determine whether the given differential equation is exact. If
it is exact, solve it.
i) (x 3 + y 3 )dx + 3xy2 dy = 0, Ans. x 4 + 4y 3x = C
ii) (y ln y − e −xy) + (1 y + x ln y) dy dx = 0, Ans. not
exact
iii) (e −x sin y − 3)dx − (3x 2 − e x sin(2y))dy = 0, Ans. not
exact
iv) (xy − 1)dx + (x...
cosxdx + [7+(2/y)]sinxdy = 0 Find if the equation is exact. If it is exact, solve....
cosxdx + [7+(2/y)]sinxdy = 0
Find if the equation is exact. If it is exact, solve.
If it is not exact, find an integrating factor to make it exact,
verify that it is exact and solve it.
1. solve the IVP: xy''-y/x=lnx, on (0, inifnity), y(1)=-1, y'(1)=-2 2.solve the IVP: y''-y=(e^x)/sqrtx, y(1)=e, y'(1)=0...
1. solve the IVP: xy''-y/x=lnx, on (0, inifnity), y(1)=-1,
y'(1)=-2
2.solve the IVP: y''-y=(e^x)/sqrtx, y(1)=e, y'(1)=0
3. Given that y1(x)=x is a solution of xy''-xy'+y=0 on (0,
inifinity, solve the IVP: xy''-xy'+y=2 on(0,infinity), y(3)=2,
y'(3)=1
14. solve the IVP: X'=( 1 2 3) X, X(0)=(0
##################0 1 4####### -3/8
##################0 0 1 ########1/4
a) Determine whether the given differential equation is exact. If it is exact, solve it. (If...
a) Determine whether the given differential equation is exact.
If it is exact, solve it. (If it is not exact, enter NOT.)
(2xy2 − 5) dx + (2x2y + 4) dy = 0
b) Solve the given differential equation by finding, as in
Example 4 of Section 2.4, an appropriate integrating factor.
(6 − 20y +
e−5x)
dx − 4 dy = 0
Consider the differential equation: y'(x)+3xy+y^2=0. y(1)=0. h=0.1 Solve the differential equation to determine y(1.3) using: a....
Consider the differential equation:
y'(x)+3xy+y^2=0.
y(1)=0. h=0.1
Solve the differential equation to determine y(1.3)
using:
a. Euler Method
b. Second order Taylor series method
c. Second order Runge Kutta method
d. Fourth order Runge-Kutta method
e. Heun’s predictor corrector method
f. Midpoint method
4(a)Verify that the equation y=lnx-lny is an implicit solution of the IVP, ydx=x(y+1)dy &
4(a)Verify that the equation
y=lnx-lny is an implicit solution of the IVP,
ydx=x(y+1)dy
y(e)=1
(b) Consider the
IVP, test whether it is exact and solve
it.
x(x-y)dy=-(3xy-y^2)dx
y(-1)=1
(c) Determine the degree of the
following homogeneous
function
(i)
f(x,y)=4x^2+2y^4
,
(ii)
f(x,y)=√5x^6-3y^6+4x^2y^4
,
Solve the differential equation by variation of parameters. y''+ y = sin^2(x)
Solve the differential equation by variation of parameters.
y''+ y = sin^2(x)
solve y' +(x+2/x)y =(e^x)/x^2 ; y(1)=0
solve
y' +(x+2/x)y =(e^x)/x^2 ; y(1)=0
Use LHopital rule to solve. lim (x-1)^(lnx) x goes to 1+
Use LHopital rule to solve.
lim (x-1)^(lnx)
x goes to 1+
Solve differential equation: y'+y=sin(x)
Solve differential equation:
y'+y=sin(x)
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