25. (2y cosx + sint x)dx sin x dy , when x =y = 1 %3D %3D

Q: 211 211 cos nx dx= [cos %3D %3D nx cos nx dx =0.

A:

Q: 26) If y=sin(-0).find dy d0

A: Given.

Q: 1. Given y= [In(3x² +8)] dy find tan(6x) dx

A:

Q: 15. Solve d²y +3 y + 2y = 3 sin x, given that when x 0, y =-0-9 Wor, OFer dx? dx dy =-0-7. dx and…

A:

Q: dy 1- IF y = cos(3 cos 2x) find dx

A:

Q: y(cos 2x)e*y – 2(sin 2x)e*y + 2x + [x(cos 2x)e*y – 3] = 0 %3D dx

A:

Q: [y²e + √elnx dy-(xy) sin² ( * O) + (---) (-) sin² tan² ,dx ey+Inx dy y(In2x-lny) -ex. dx = 0

A: We can solve this using substitution method of ordinary differential equation

Q: 1 (5* )csch dy if Find dx 1. (а) y x>0. (ecosh 5x ) In Vx +1 d Show that for x 2 1, coshx- dx (cosh²…

A:

Q: z = y sin(2x) + (1 + x²)e* + cos x tan¬(y* + 1) In(y6 + 137)

A: ∂z∂x=∂∂xysin2x+1+x2ex+cosxtan-1y4+1lny6+137=∂∂xysin2x+∂∂x1+x2ex+∂∂xcosxtan-1y4+1lny6+137=2ycos2x+1+x…

Q: 7. Differentiate w.r.t x- sin 5x cos 3x 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A:

Q: 4. (y? cos x - 3x²y - 2x) dx + (2y sin x - x3 + Iny) dy = 0, when x = 0, y = e

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

Q: 4. (3sin y- 5x)dx +2x cot ydy = 0 Ans. x'(sin y-x) = csin²y

A:

Q: 4. (y² cos x - 3x²y – 2x) dx + (2y sin x – x³ + Iny) dy when x = 0, y = e %3D 5. (x² – 1) dy = ((1 +…

A:

Q: 4) Find when y? - x2 + cos(x + y) = 0 %3D dx

A:

Q: 4. ["s 0 sinx + 2 cos x dx

A:

Q: 211 211 S cosr nx dx= | [cos nx cos nx dx = 0. %3D

A: The detailed solution is as follows below:

Q: 4. ſ cos xesinx dx

A:

Q: 1 E valuate [ (x' + cos(3x)) dx sin (3x) a) b)

A:

Q: 8/ (e* sin y +3y)dx -(3x-e* sin y)dy = 0

A: Given thta  The differential equation

Q: 1. Solve for y of the Separable D.E. sinx dx +y dy = 0

A: To solve the given differential equation for y.

Q: 25 a²y(cos(Tz) +2) dæ dy dz

A:

Q: What is the solution of the equation dey/dx=y/x+tany/x

A:

Q: Find dy/dx for y = 3l(sin-(e-3**)12 dy 3(sin"(e-*)* In3 2(sin-"(e-3x*)- dx 1(-6х) V1-e-6x2

A:

Q: 4. (y² cos x - 3x²y - 2x) dx + (2y sin x - x³ + Iny) dy = 0, when x = 0, y = e

A: exact differential equation

Q: 1. Given [In(4x² +7)ľ° y= find dx dy tan(5x)

A:

Q: dz Find x? sin(2y – 5z) =1+y cos(6zx) -

A: This is partial derivative so differentiate it as normal differentiation of z with respect to y…

Q: 3. Evaluate 2y²sinxy dy dx 4. Evaluate , S sin(x² + y²) dy dx

A:

Q: トキ 4 Sin Yx cos? dn SinYy

A:

Q: 1. If y = sin x² x =²), ex find dy dx

A: Given y=sinx2-xex To find dydx

Q: 4- Find dy/dx for y = 3l(sin-(e-3x')1² dy 1(-6x) = 3(sin-(e-3*" )I* In3 2(sin¬1(e¬3x²) dx In3…

A: Given y=3sin-1e-3x22

Q: (c) Solve the IVP x(1- siny)dy = (cosx – cosy – y)dx.

A: Given,          x(1-siny)dy=(cosx-cosy-y)dxand            yπ2=0

Q: 2. 2メ dy dx for y = Cos (ln x + e put lに

A: y = cos2(ln(x) + e2x)

Q: 4. J S (esc²a – co sec 0 tand) d0 - -

A: Explained below...

Q: HW 0If y=tanx show that- yl" =-2 Siny coży

A:

Q: 11. (e* sin y – 3x²)dx + ( e* cos y+ |dy = 0 12. (2x + 1+x?y? ) dx +( -29) dy = 4 - 29) dy = 0…

A:

Q: 3) I Cos dydx Ins Iny 4) S S e** dxdy X 1 0

A: 3)  Given:      ∫π2π∫0x21xcosyxdydx       =∫π2π∫0x21xcosyxdydx

Q: 4- Find dy/dx for y = 3[(sin-(e-3x*)1² dy 3(sin-(e-3*)1* In3 2(sin-'(e-3**) 1(-6x) %3D dx V1- e-6x2

A:

Q: 9. (siny - ysinxy)dx + (xcosy-xsinxy)dy 0

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

Q: Find dy dx 12) y = cos ³ (5x+2) -2)) y = √tan √√₂x + + 3)) Por The following Function i y = sin-¹…

A: **As per our guidelines, we are supposed to answer only 3 subparts of a question. Since you have…

Q: I sin 2 dy dx (x² – y) dy dx 5. 6. x? – y² dy dx 8. L ellyt dx dy 7.

A:

Q: π/3 7. Sp² sin 0 de dp π/6 8. (2-y)dy dx 9. 5/¹¹² x cos y dz dx dy

A: Since you have posted multiple sub parts question in this question which are not interlinked so i…

Q: 4- Find dy/dx for y = 3(sin-(e-3x²))2 dy 3[(sin-{(e-3*)i* In3 2(sin-1(e-3**) - 3x2 1(-6x) dx V1-…

A: Differentiate term by term

Q: dx 3. 2y cos x + 4y sin x = sin 2x, given y =0 when x n/3.

A:

Q: 3) [ - cos dydx X X In 8 In y 4) S S e**y dxdy

A: (3) we have to evaluate ∫π2π∫0x21xcosyxdydx let  u =yx ⇒dudy=ddyyx         =1xddyy=1x⇒du = 1xdy…

Q: (2e" sin(y) – 4y)dr + (–7x - e cos(3)dy = 0 not exact

A:

Q: 4- Find dy/dx for y = 3(sin-(e-3x*)2 dy 31(sin-(e-3*")r* In3 2(sin-'(e-3x")- dx 1(-6х) е 1 - e-6x2

A:

Q: 1- Cosh x dy + (y sinh x +e*) dx =0

A:

Q: 10. Find dy/dx of y= 1/ (tan-1 x)

A:

Q: If y = (4x² – 3x+ 2)(e2* – cos 3x), then find dy at x = 0. dx -2x %3D - -

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.