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solve following second order ode numerically matlab

By SK Math Expert August 21, 2021Advanced Math, Numerical Analysis, ODEs

Question : Solve following second order ode numerically matlab \[\frac{d^2y}{dt^2}+\frac{dy}{dt}+y=2t+3\sin{\left(t\right)} , y\left(0\right)=2,\ y^\prime\left(0\right)=3 \] in the interval [0, 10] and plot the solution. Solution : To Solve given second order…

how to convert following second order ode into a system of first order ODEs

By SK Math Expert August 21, 2021Advanced Math, Numerical Analysis, ODEs

Question ; Convert following second order ode into a system of first order ODEs \[\frac{d^2y}{dt^2}+\frac{dy}{dt}+y=2t+3\sin{\left(t\right)} , y\left(0\right)=2,\ y^\prime\left(0\right)=3 \] Solution : Given second order ODE \[\frac{d^2y}{dt^2}+\frac{dy}{dt}+y=2t+3\sin{\left(t\right)} \] (1) Subject to…

solved If the straight line y = mx lies outside the circle x^2+y^2-20y+90=0 then the value of m will satisfy

By SK Math Expert August 20, 2021Abstract Algebra, Advanced Math, Geometry, Linear Algebra, Mathematics, Multivariable Calculus, Real Analysis

Question : If the straight line y = mx lies outside the circle x^2+y^2-20y+90=0 then the value of m will satisfy Solution : If the straight line y = mx…

what is dimension of the vector space C(R) of the complex numbers over real

By SK Math Expert August 20, 2021Abstract Algebra, Advanced Math, Complex Analysis, Linear Algebra, Mathematics, Multivariable Calculus

Question : What is The dimension of the vector space C(R) of the complex numbers over real numbers ? Solution : We know that a complex number z is written…

limit tan^-1(x)/x as x approaches 0

By SK Math Expert August 20, 2021Abstract Algebra, Advanced Math, Mathematics, Multivariable Calculus, Real Analysis, Trigonometry

Question : Find the limit tan^-1(x)/x as x approaches 0 Solution : We shall let the limit is \[L={\rm limit}_{x\rightarrow0}{\frac{\tan^{-1}{\left(x\right)}}{x}} Since \tan^{-1}{\left(0\right)}=0\ Hence \frac{\tan^{-1}{\left(0\right)}}{0}=\frac{0}{0}\] We can apply L’Hospital rule, that…

limit of sin^-1(x)/x as x approaches to 0

By SK Math Expert August 20, 2021Advanced Math, Linear Algebra, Multivariable Calculus, Real Analysis, Trigonometry

Question : limit of sin^-1(x)/x as x approaches to 0 Solution : We shall let the limit is \[L={\rm limit}_{x\rightarrow0}{\frac{\sin^{-1}{\left(x\right)}}{x}}\] Since \[\sin^{-1}{\left(0\right)}=0\ Hence \frac{\sin^{-1}{\left(0\right)}}{0}=\frac{0}{0}\] We can apply L’Hospital rule, that…

limit of sin^-1(xy-2)/tan^-1(3xy-6) as (x y) approaches to (2 1)

By SK Math Expert August 20, 2021Advanced Math, Mathematics, Multivariable Calculus, Real Analysis, Trigonometry

Question : Find the limit of sin^-1(xy-2)/tan^-1(3xy-6) as (x y) approaches to (2 1) \[{\rm limit}_{\left(x,y\right)\rightarrow(2,1)}{\frac{\sin^{-1}{\left(xy-2\right)}}{\tan^{-1}{\left(3xy-6\right)}}} \] Solution : We shall let the limit is \[ L={\rm limit}_{\left(x,y\right)\rightarrow(2,1)}{\frac{\sin^{-1}{\left(xy-2\right)}}{\tan^{-1}{\left(3xy-6\right)}}}\] Multiplying and…

The equation of a right circular cone with vertex at the origin the axis x-axis and semi-vertical angle pi/4 is

By SK Math Expert August 20, 2021Advanced Math

Question : The equation of a right circular cone with vertex at the origin the axis x-axis and semi-vertical angle is Solution : Let P(x, y, z) be any point…

The equation of a right circular cone with vertex at the origin the axis z-axis and semi-vertical angle pi/4 is

By SK Math Expert August 20, 2021Advanced Math

Question : The equation of a right circular cone with vertex at the origin the axis z-axis and semi-vertical angle is Solution : Let P(x, y, z) be any point…

how to Find sinh(x+iy) formula

By SK Math Expert August 19, 2021Abstract Algebra, Advanced Math, Complex Analysis, Computer science, Mathematics, Mechanical Engineering, Multivariable Calculus

Question : Find sinh(x+iy) formula Solution : Let the complex number as \[z=sinh\left(x+iy\right)\] We know that \[\sin{\left(iz\right)}=isinh\left(z\right)\] So we shall multiply and divide by i we get \[z=\frac{isinh\left(x+iy\right)}{i}=\frac{\sin{\left(i\left(x+iy\right)\right)}}{i}=\frac{\sin{\left(ix-y\right)}}{i}\] Now we…

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