6x? (6+x)y"+ 4x (6 +x )3 y' -u (36-X2) y =0 If the roots of the indicial equation Correspording to the regular Singuler pont X = 0 of the following differenttal equation are and 2, evaluate ritrz+ z Answer: -27

Q: Find the solutiTon of followina ordfnarg differentral equation -2x

A:

Q: Show that the curve y = x? sin 3x touches the parabolas y = x andy =-x² alternately at infinite…

A:

Q: Find a parametrization of the right branch (x > 0) of the hyperbola(x/a)2−*(y/b)2= 1 using cosh…

A: Given that. xa2-yb2=1     ...(1) Need to evaluate parametrize form of (1).

Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, z = cos 3t at the…

A:

Q: A The roots of Characteristic equetion f oreler, lineor homopeneous-equation with constant…

A:

Q: A cantilever beam of length L is embedded at its left end. Find the deflection of the beam when w(x)…

A:

Q: Determine the surface of revolution of arc y³+y=x²+6x on the interval [-5,-1] if it is revolved…

A: Use the formula of arc length to determine its length. Now use to it determine the volume generated…

Q: Q2\ Shoe that another from of Euler- * Lagrange equation is : L, -L,½ -y'L,ý - y"L,51 = 0 . - y 'Ly5…

A:

Q: 8. At what point of the parabola is the tangent line parallel to 7x+y-2=0? y = 2r-3x +1 O (1,0) O…

A: Here is the solution:

Q: Sketch the solid described by the given inequalities: 0<=r<=2, -pi/2<=theta<=pi/2,…

A: First draw the first two inequality 0<= r <=2 and –pi/2<= theta <= pi/2 in the…

Q: If the foundation of a structure with a degree of freedom is affected by displacement with the…

A: Given:- U g(t)=10 sin (30t)

Q: (a) S,(Iz – il2 – z) dz along the semicircle y = 1+ et“, 0 < t < n; -

A: ∫γz-i2-zdz=∫0π1+eit-i2-1-eitieitdt=∫0π1+cost2+sint-12-1-eitieitdt=∫0π1+cos2t+2cost+sin2t+1-2sint-1-e…

Q: 4. By revolving the semicircle x = cost, y = sint (0 <t< ) about the x-axis, show that the surface…

A: Equation of semicircle with radius r is x=rcost, y=rsint We know the formula for surface area for…

Q: Find the points on the surfaces x^2-yz=25 that are closest to origin

A:

Q: 1. Point K is located at (4. 2, 0. 3)and point Lis located at (5. 8, -0.6). What is the location of…

A:

Q: The roots of Characteristic equetion of a thrrd oreler, lineor homapeneous-equation with constaut…

A: Consider homogenous differential equation with constant coefficient:…

Q: The value of cosh(3z+1)dz, where C is the line segment from z=1 C to z= 2i. O a. (-sinh(6i+1)+sinh…

A: We have to find the value of integral,  I = ∮Ccosh(3z+1)dz  ;  where C is the line segment from z=1…

Q: Find the exact value of | (yi+ vxj) · dr where C is the parabola y = x² from the origin to the point…

A:

Q: The force on a particle is described by 2x3 - 4 at a point æ along the a-axis. Find the work done in…

A: The force on a particle is described by 2x3 -4 at a point x along the x-axis. Find the work done in…

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 = 0 that are closest to the origin. please…

A:

Q: The area bounded by the parabolas (x − 2)^2 − 9py=0 and y^2=9p(x−2) is to be revolved around x = 2.…

A:

Q: 12. Find an equation for the tangent plane to the surface given by 2xy? = 2z2 – ryz at the point (2,…

A: We know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Where n→-nxi+nyj+nzk is…

Q: Find the roots of 5sin^2x-8cos^5x=0, x_0=0.5, using Newton method

A: Concept Used: Newton Method xi+1=xi-f(xi)f'(xi+1) Consider 5sin2(x)-8cos5(x)=0So…

Q: Find the lateral​ (side) surface area of the cone generated by revolving the line segment ​y=2x/5…

A: The given line segment: y=2x5 ;       0&lt;x&lt;8

Q: 6 of 9 > Find an equation of the tangent plane to the surface at the given point. 2x² + 2y² + 4z² =…

A:

Q: Find the lateral surface area of the cone generated by revolving the line segment 5x-8y+40=0 about…

A: Find lateral surface area.

Q: 44. Find a parametrization of the right branch (x > 0) of the hyperbola 1 - using cosh t and sinh t.…

A: The equation of hyperbola is xa2-yb2=1   The right branch (x&gt;0) of the hyperbola can be…

Q: Solve x = cosr for solution exact to 3D by Newton’s method (with xo = 0) and bisection method…

A:

Q: Find the approximate roots of y = r - a +x – 3 between r = 2 and z = 2.5 by using either the…

A: Bisection method: Let f(x)=0 be equation, to find the roots of equation in interval a,b. Let us…

Q: Find the points on the surface y2 = 4 + xz that are closest to the origin. (Enter your answers from…

A: Consider the given surface equation y2=4+xz.  The distance d between the origin 0,0,0 and any point…

Q: Give two examples of the situation with the solution clearly and in order Soperties of Bessel's…

A:

Q: Determine the largest interval in which the unique solution of (t- 3)y +tanty = t, y(m)3D0 is…

A:

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 =0 that are closest to the origin. please…

A: The parametric equation of hyperbolic cylinderx2-z2-1=0 is , x=cos hθ                          y=y…

Q: Find the root of the cubic equation 4x3 + 3x2 – 8x – 2 = 0 in the domain [ 1 , 2 ] using numerical…

A: According to the fundamental theorem of algebra, every algebraic equation has a root. If the…

Q: 9. In the ry-plane, a particle moves along the parabola y = x? – x with a constant speed of 2/10…

A: Given:-  In the xy-plane, a particle moves along the parabola y = r²r with a constant speed of 2√10…

Q: Find the root of the cubic equation 4x3 + 3x2 – 8x – 2 = 0 in the domain [ 1 , 2 ]  using numerical…

A:

Q: . (a) Show that as (x, y)→ (0, 0) along any straight line y = mx, or along any parabola y = kx², the…

A: Given : f(x) = x³y/(2x^6+y²)  To find : To prove that limit exist along parabola

Q: -2n de 24. Show that 2n. V2-cose

A: We have to prove given identity:

Q: 3. Find how many roots the equation 2z4 – 323 + 3z² – z + 1 = 0 - - has in the right half-plane Rez…

A: Given: 2z4-3z3+3z2-z+1=0

Q: Use the Least square approximation to fit the function sin (0.5x) on the interval [0, T/2] by a…

A: Consider the given: f(x)=sin(0.5)x             0≤x≤π2g(x)=y=ax+b

Q: 1 Find the area of the surface generated by revolving the curve x = cos (3t), y 3+sin (3t) on 0sts…

A:

Q: Find the length of one arch of the cycloid x= 5(t-sin(t)), y= 5(1-cos(t)).

A:

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T =…

A: We have given; The temperature T at any point (x, y, z) in space isT = 400xyz2and the unit spherex2…

Q: Suppose that the Celsius temperature at the point (x,y,z) on the sphere x +y +z =1 is T= 1600xyz“.…

A: This is a problem related to maxima and minima. Based on the general formula we will answer the…

Q: Find an equation of the tangent plane to the surface at the given point. 4x2 + 2y? + 4z? = 22, P =…

A:

Q: In the figure to the​ right, the equation of the solid curve is y equals StartFraction secant…

A:

Q: of the solid in revolution as it axis and the function 2 – x) 0<x< 2

A: The given function is fx=x2-x,    0≤x≤2. Find the volume of the solid in revolution as it rotates…

Q: 10. Find the surface area of the solid generated by revolving the line segment y = vx + 1 , 1 < x <…

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.