y = secx prove that d² y dx +y 2y

Q: d'y & dx Find d'x to the : dy *yーy=7 %3D7

A: We have the expression x2y2-y=7. Differentiating both sides of this equation with respect to x, we…

Q: 3. f 3/2 y dydx (I wz dx dy dz. 4.

A:

Q: fo axy dx + 2xy dy, where Cis the rectangle bounded by x = -1.x = 1, y = 1, and y = 5. 6xy dx + 2xy…

A:

Q: Evaluate the integrals

A: ∫01∫0x2∫0x+y2x-y-z dz dy dx

Q: dy Find - for y = du dy du = = [19+ √9 +10t2 dt. 0

A: given y=∫0u9+10t2dtTo find: dydu

Q: t2 + y? = ty dt

A:

Q: Q/ find the dy when y = (x+z)= リ=(メ+2)mx, %3D 2x Qul Fird dy すく e y= ノ

A: Answer

Q: dy_ 1-y dx V1-x? V1-x' +/1-y? = a(x - y), then show that %3D

A:

Q: dy If x = t - t3 and y = t2 - t, the value of at t = 2 is %3D %3D dx

A:

Q: 7y f(x, y) = tan a² f dx² dy? dzðy dydr

A: From the given problem:   fx,y=tan-17yx   (a) As we know: ∂2f∂x2=∂∂x∂f∂x So, ∂f∂x=∂∂…

Q: dy Find for y = dr dy dr || r J√3 + 0 3 + 4t2 dt.

A:

Q: dy dt2 dt d'y 8x = 0 - dt?

A: Given that, d2xdt2+dydt=0d2ydt2-8x=0 Now take the derivative for the first equation with respect to…

Q: d'y Calculate y = eX + e* dy %3D dx2

A: It is known that if  we have a function f(ax) then the derivative of the function is,   Here it is…

Q: zl*dz, where C is x(t) t2, y(t) , t:2 1 Evaluate /=

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 2. Show that the function u p(ry) + Vry v(y/x) provides the equation Pu = 0. ду? dx²

A:

Q: dy +y de : 2 et dx Arowar 1- ye" (c -x*) 1= yet (c -x*) %3D

A:

Q: Given 2tanx +4y=4, find 1. dy %3D dx secx a. 2 b. sec'x C. 2sec'x 2.

A:

Q: Ify = x(t) +3, then which statement is true? O y(t) = = 2 dy dz O y (t) = (告) %3D O y (t) = df(z) O…

A: Given : y = xt + 3

Q: 1. xdy y(1+ Iny- In x) dx

A: Note:-  as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Evaluate . y? cos(x) dx + 2ysin(x)dy where C is the straight line between (0,0) and

A: The equations of the straight line joining (0,0)to π2,1 are x-0π/2-0=y-01-0=t(say) i.e. xπ/2=y1=t…

Q: dy If x = 3t2, y = t³ then %3D dx II

A: Here we find out the dy/dx

Q: 4 J4- y ktx dy S[S( x, y) dA = [] 3 R 0 2- 2 2

A: Consider the given expression, ∬Rfx,ydA=∫04∫2-y24-yx2-x33dxdy This suggests that the region spans…

Q: <plain why y = t² – sin? t cannot be a solution to y" + p(t)y' + q(t)y = 0 nere and q are both…

A:

Q: dt2 d²y e. ++ 4y = 8t – 10, y(0) = 1, y'(0) = 7 %3D %3D %3D

A: As you post multiple questions According to the guideline I only solve the first problem. Please…

Q: (e) dy if y = (t +1)(t + 9) %3D dt It%3D3

A: Given that y=(t2+1)(t+9)

Q: Show that if y = cosx/x , then d^2y/dx^2 + 2dy/dx+ y = 0

A: y=cosxx Differentiating with respect to x, we get dydx=dcosxdx·x-dxdx·cosxx2…

Q: dy where C is defined by dx + x2 + y? Evaluate x2 + y? C T(t) =,0 <t< 2n

A:

Q: dy dx +y =xy², y(0)3D 1/2

A:

Q: dy if Exercises (20.5): Find dx 1) r*y + 2) %3D

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Solve the IVP for y(æ): dy + dr y = 19y", y(1) = 1 y(z) =

A:

Q: 2 5. x = 1+t2 2 y= t(1+t?)

A:

Q: Solve for y(t) where y(t) + 2 / a – u)y[w)du = t.

A:

Q: y'dx-(sy + y* }ky = 0 1. Let the substitution y=2; y=vx; dy=vdx + xdv

A:

Q: Find - given that dt dx x? + y? = 2x + 4y, x = 3 y = 1, and dt 11 dy i dt II

A: Given problem is :

Q: (ztan 2 +1) dx – x dy = 0

A:

Q: f(x, y) = 2x- xy + y, find (a.)and (b.) at (Xo, yo) didirectly from the definition. dx dy

A:

Q: dx Find the value of at y=1 if x=z³+4z and z= dy (y? + 2y)²/3.

A: Given,         x=z3+4z  and  z=y2+2y23

Q: J(y) = (y/(x) + y(x))² dx, for all y E V.

A: In this question, the extremal is given as J(y)=∫01(y'+y)2dx the class  A={y∈V|y(0)=0,y(1)=1}

Q: 3e2º sec 20 dy determine de Given y = V(0-2)

A:

Q: d?y e. dt? dy + 4y = 8t – 10, y(0) = 1, y'(0) = 75 %3D dt 2

A: As you asking multiple questions so I answered only first

Q: dy y3Dx dx Inx Find

A: y=xlnxTo find dydx

Q: dy Find dt y = 3t(21 – 5) $ II 히

A: The product rule of differentiation states that ddx[f(x)g(x)]=g(x)ddxf(x)+f(x)ddxg(x) The chain rule…

Q: dy %3D dx sec? x sec y

A:

Q: y = x*, d'y 1 dy dx y dx, Prove that Y = 0. X

A: First we find out dy/dx then d2y/dx2. And put the values of dy/dx and d2y/dx2 in given condition.

Q: Find the I.F of y(2x-y+1)dx+x(3x-4y+3)dy=0.

A: Given equation is y2x-y+1dx+x(3x-4y+3)dy=0

Q: dy Find at z da 2 and u = (2x + 1)ª. 0 given y = u + ·

A:

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.