Use Separation of Variables to find a solution in the domain (-∞, 1] with h(1) = 0.

Q: At which iteration shows that the root of a nonlinear equation is Xr = 1.2021 when a = 2 and b = -1…

A: We need to find at which iteration shows that the root of a nonlinear equation is Xr = 1.2021 when a…

Q: What do you mean by Separable Equations?

A:

Q: Find the number of non negative solutions to x+y+z= 21. With the conditions that x < 3, y ≥ 2, z ≥…

A: Given that x+y+z=21 with the conditions x&lt;3, y≥2, z≥4

Q: Obtain the general solution valid near the origin: х(х-2)y1+2(х-1)у - 2у %3D0

A:

Q: Determine the interval in which solutions are sure to exist. !!! y (4) + 3y + 2y = t Valid on the…

A:

Q: 8x²y" + 10xy' – (1+ x)y = 0

A:

Q: (² + 1)³yy'(t) = 1(y² + 4)

A: Given:- (t2 +1)3y y'(t) =t(y2 +4)  To find:- General solution of given differential equation

Q: Find the solution of 2y-y² sec²(xy²) + (2x − 2xysec² (xy²))y' = 0 given y(1) = 2.

A:

Q: y" - 6y' + qy 2,

A:

Q: a) Solve y' = 3x² + y, y(0) = 4 by choosing step length 0.1 for y(0.2) by Euler's improved method

A:

Q: x(x – 2)y" + 2(x – 1)y' – 2y = 0

A: Solution: x(x-2)y"+2(x-1)y'-2y=0 Solve using the series method: A linear homogeneous ODE with…

Q: y' = x – 4y %3D

A: The solution of above differential equation is written below.

Q: 2y”” − 3y" — 3y² + 2y= (e* + e*)²

A:

Q: Obtain the general solution valid near the origin: x(x − 2)y" + 2(x − 1)y' − 2y = 0

A:

Q: 2x2 + 2x + 11 dx J (2x + 3) (x² + 4)

A:

Q: Solve for all possible solution in the equation y^2 + y = x + Inx + e^y - x^2, using Secant Method *

A:

Q: – kz = 0, -z= 0, solution then

A:

Q: (x) + Find the general solution аху- х+у о у-xlncxЈtc 2 x² Ў= х²-хутуг у-х- х Нихте з y = x + y + y…

A:

Q: Use variation of parameters to find a particular solution of y"- 2y' +y = 14xie" Yp(x)

A: y''-2y'+y=14x32ex find the roots for the homogeneous system  r2-2r+1=0 r-12=0 r-1=0 r=1 for one real…

Q: Use Fixed-Point method to find solution accurate to within 10 for the following nonlinear equation:…

A: Given equation is, The given initial solution is,  To find the solution of the given equation…

Q: Find the general solution for the homogenous equation of y′′ − y′ − y = 0.

A:

Q: use Separation of Variables to find the general solution. yy' = x

A:

Q: Obtain 2 linearly independent solutions valid near the origin for x>0 2хy" + 5(1 — 2х)у' — 5у %3D 0.…

A:

Q: Use variation of parameters to find a particular solution of y"- 2y' + y = 14xie Yp(x) =

A: Auxiliary equation for the given equation:

Q: use the two phase method to solve the lp MAX -  4x1  +  x2 - 2x3 st --    2x1 + 2x2 + x3 = 4 x 1+…

A: We can solve this using two phase method

Q: Solve for all possible solution in the equation y^2 + y = x + Inx + e^y - x^2, using Secant Method

A: We have the following equation in two variables : y2 + y = x + ln(x) + ey - x2   As there are two…

Q: Q2/ solve :- +2y = Sin 3 X %3D u sing (D-operator methoD)

A:

Q: Solve with help of partial fraction technique (b) f (5 – 4 x – x² ) dx

A: Our Aim is to solve the integral given below with the help of partial fraction:-∫x5-4x-x232dx

Q: 9 y y' - -y x2 and find the solution that satisfies y(1) = 1.

A:

Q: Verify that y = h(x) =- (C is an arbitrary constant, x # 0) is a solution of xy' = -y.

A:

Q: Find the general solution and the particular equation of the Equation Linear 2ª order given the…

A: We have to be find solution

Q: x²y = 1+ cx

A: the given equation is x2y=1+cx

Q: 7. Verify that y = x2 - 1 is a solution of (y')* + y? = -1.

A: Given- y=x2-1 To verify- That the above function is the solution of y'4+y2=-1.

Q: Solve the particular solution (D2 + 3D + 5)y = 5e-x sin (2x) using D - operator method.

A: We find the particular solution of  (D2 + 3D + 5)y = 5e-x sin (2x) using D - operator method.

Q: Obtain the particular solution. y' = x exp(y-x²) ; when x = 0 , y = 0.

A:

Q: Find a particular solution to æ' = -x – y + e', y' = 2x + y – ešt using undetermined coefficients.

A:

Q: b, Solve dy- y -n3y²--x5 finding particular solution.

A: Solve DE

Q: 5- Find the particular solution for: 2e2x – y = xy', x = 1 when y = 6 %3D

A:

Q: A. y" – 2y + 1 = (x + 1)e²x

A:

Q: 2 ydx = 3xdy; when x = -2, y = 1 Ans. y = (x/2)3

A: Given: 2ydx=3xdy ; x=-2, y=1   We know that; ∫1ax+bdx=1alnax+b+C

Q: Find the Particular Solution indicated. (Homogenous Linear Equation with Constant Coeffiecients)

A: Given : Homogenous Linear Differential Equation with Constant Coefficients               D2+D-12y=0…

Q: 6- Show that y = xsinx is a solution to y +y 2cosx

A: The given differential equation is: y''+y=2 cos x

Q: f(x) = e¬x² + lIn 2 + 32×

A: Given,      f(x)=e-x2+ln2+32x

Q: 2. x (х — 2)у" + 2(х — 1)у' — 2у %3D 0 |

A: Power series solution of the differential equation

Q: (2х + 1)у" — 2у - (2х + 3)у %3D (2х + 1)2; У1 —е-*

A:

Q: Use separation of variables to find an explicit solution. xyy' = 2xy 2 2 + y?

A: using seperation of variables  and then integrate....

Q: Obtain the general solution valid near the origin: x(х — 2)у" + 2 (х — 1)у' — 2у 3D0

A: The differential equation has singularity at the origin. So we find the solution by Frobienius…

Q: Use variation of parameters to find a particular solution of y'' - Y = 4e-x 1-e-2x Yp (x) =

A: Solution of the differential equation, By using the method of Variation of perameters

Q: Use variation of parameters to obtain the general solution. y''+4y = 4 sec2x

A: The given differential equation is; y"+4y=4sec2x.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.