3. Find the general solution to (assume x and y are the only variables) (a) y' = ky (b) y' = k – y (c) y' = ky²(1+x²) (d) y' = 2xy sin(x²) y In y %3D (e) y'

Q: 9.(x−2)y′′+y′+(x−2)(tanx)y=0,y(3)=1,y′(3)=2

A: Given: (x−2)y′′+y′+(x−2)(tan x)y=0,y(3)=1,y′(3)=2 To Find: The longest interval in which the given…

Q: 3. Solve for y in the equation y = e* sin x + e* cos x - y +c

A: the given equation is y = ex sinx + ex cosx - y +c

Q: If r(2) = sin(z² – 10z + 16), find r' (z) =

A: Since, we have been given that r(z)= sin(z2-10z+16)Our Aim is to find r'(z)=?

Q: 3-2r . Find y'(0) %3D

A: Given: y=3-2x21+x To Find: y'0=?

Q: The solution of 1y"+ y' = 0, y (0) = 0, /(0) =1 /(0) = 1 %3D is y(a) = %3D (A) cos a (B) sin a (C)…

A: The solution of a differential equation must satisfy the differential equation. Check the options…

Q: y = x"^, x > 0 Inx-1 Inx Inx C. y'= 2lnx x' „Inx-1 D. y'= 2lnx x" „Inx-1 A. y'= x B. y'= 2 x'

A: SOLUTION-

Q: b) y"+ 4 y = cos (t), y(0) = y'(0) = 0

A:

Q: 1. If y = In(V x² +1 ) , then y' = 2x (b): 2x (a) x² +1 3(x2 +1) () 3(x2 +1)-2/3 (d) 3(x2 +1)

A: y=lnx2+13⇒y=lnx2+113⇒y=13·lnx2+1   ∵lnxy=ylnx

Q: (3x² − 2xy + 2) + (6y² − x² + 3)y′ = 0

A:

Q: Find the general solution of the equation xy' = ky that is valid for x > 0.

A: We have to find y(x) for this equation which is valid for x>0. We use integration to solve this…

Q: cos(x) * еУ + 9у %3D Зу8 — 5х + 10е =

A: The expression cos(x)×ey+9y=3y8-5x+10e. We have to find y' or dydx.

Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: (a) a²y + y sin r = xy. (b) y = x³y - 2y³. (c) y = e²-2y (d) y'= x² + y² xy

A:

Q: G(y) = (y − 1)4 / (y2 + 2y)7 Find G'(y) =

A: for a polynomial function of power n: Division rule of differentiation:         Chain rule :…

Q: 3. (1−x³) d²y dx² DE -+ (sin x)y' − 3xy = ln x(+1) TYPE ORDER DEGREE LINEARITY

A: Need to write down the type, order, degree and linearity of the given differential equation.

Q: 10. If cos(x + y) = 2x- 2y, find y'.

A:

Q: (1+x)y' + y = cosx; y(0) = 1

A:

Q: z(x) 1+x² You need to find the formula for y'(x) first, then evaluate y'(x) at x = (c) Let y(x) = =…

A:

Q: 1. y' = 2(3x + y)? – 1; y(0) = 1

A: Given that: y'=2(3x+y)-1, y(0)=1

Q: Find y as a function of a if y" − 3y" − y + 3y = 0, y(0) = −9, y'(0) = −8, y'(0) = 7. y(x) =

A:

Q: (d) If x y/1-y², find

A: Solving question1 for other question repost.

Q: 1) Show that (a) y =xe satisfies the eq. xy' (1-x)y (b) y =xe"A satisfies the eq. xy'=(1-x²)y

A:

Q: 2. y" + y' = cscx %3D

A: 2. we have  y''+y'=cscx  first find C.F m2+m=0m(m+1)=0m=0,-1y(x)=c1e0x+c2e-x=c1+c2e-x

Q: If x²y + y²x = 6, then find y' at x = 2.

A:

Q: 2. Find the general solution. y' + sec x y = cos x. а. b. y' +y =÷(e* -e-*).

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.