Solve - MathStudio Manual

Solve(f(x), x, [guess])

f(x)

The expression to solve.

x

The variable to solve.

[guess]

The initial guess value to solve the equation. If a list of two values is given such as Solve(sin(x)=0,x,[0,6@pi]), Solve will return the solutions within the given range.

Description

Solves the expression for the given variable.

When no equals sign is given, Solve assumes the expression is equal to zero. For example, Solve(x^2-3) will solve the expression as x^2-3=0.

Quadratic equations can be solved by entering each coefficient as a parameter. For instance, Solve(5x^2+3x+4) may also be entered as Solve(5,3,4).

Solve can also solve a system of equations.
Solve(equation1, equation2, equation3, ...)

Examples

Linear equations

Solve(3x+5=0, x)

Solve(3x+5)

Quadratic equations

Solve(x^2-5x+6=0)

Solve(1, -5, 6)

Solving a system of equations

Solve(x+y+z=5, x+2y=6, z-x=3)

Solve(x^2+y^2=25, y^2=x^2+3)

Solve(y=x^2, y=8-x^2)

Solve(3x-y=-2, 2x^2-y=0)

Solve(3.3330x+15920y+10.333z=7953, 2.2220x+16.710y+9.6120z=0.965, -1.5611x+5.1792y-1.6855z=2.714)

More examples

Solve(x^6+16x^3+64, x)

Solve(sin(3x)+cos(3x)=0)

Solve(4sin(x)^3+2sin(x)^2-2sin(x)=1, x)

Solve(3*tan(x)^2=1, x)

Solve(exp(3x)=2, x)

Solve(tan(x)^2=3)

Solve(ln(x)=1, x)

Solve(3sin(x)+exp(x)=2, x, [-2@pi, 2@pi])

Solve(asin(x)=@pi/4, x)

Special functions

Solve(Si(x)=1/2)

Solve(BesselJ(0, x)=2/3)

Solve(LegendreP(3, x)-1=0)

Solve(Gamma(x)=5040, x, [1, 10])

Related Functions

Eval, SolveSystem

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Functions

A

AlternatingSeries(n, [terms])

Angle(A, B)

Animate(variable, start, end, [step], [value], [fps])

Apart(f(x), x)

Append(expression1, expression2)

B

BarPlot(list1, frequency1, ...)

Bernoulli(n, [z])

BesselI(v, z)

BesselJ(v, z)

BesselK(v, z)

BesselY(v, z)

Beta(m, n)

Binomial(n, r)

BinomialCDF(n, p, x)

BinomialPDF(n, p, x)

BodePlot(function, variable, minimum, maximum, mode)

BoxPlot(x, [frequency1], [x2], [frequency2], ...)

Button(name, [list], [value])

G

GCD(n1, n2)

GegenbauerC(n, a, z)

GeoCDF(p, x)

GeoPDF(p, x)

Gradient(function, [varlist], [mode])

Gudermannian(z)

H

HalfRectSineWave(x, [T])

HankelH1(v, z)

HankelH2(v, z)

Harmonic(z)

Heaviside(x)

HermiteH(n, z)

Hessian(function, [varlist], [mode])

HRStoHMS(hours, [digits])

http(url, [filter])

Hypergeom_2F1(a, b, c, z, [mode])

J

Jacobian(function, [varlist], [point])

json(data, [filter])

JuliaPlot(expression, ...)

K

KelvinBei(v, z)

KelvinBer(v, z)

KelvinKei(v, z)

KelvinKer(v, z)

M

Matrix(rows, [columns])

MatrixLU(matrix, [mode])

MatrixMap(matrix, name, [value])

MatrixQR(A)

MatrixSVD(A)

Max(number, ...)

Mean(list)

MedianFit([x], y)

MedianFitModel([x], y)

MedianFitPlot([x], y)

Message(string)

Min(list)

Mod(m, n)

Multinomial(nList)

MultiPlot(plot1, plot2, ...)

MultiPlot3D(expression, ...)

N

nCr(n, r)

NIntegrate(f(x), x, a, b)

NormalCDF(lower, upper, [mu], [sigma])

NormalPDF(x, mu, sigma)

nPr(n, r)

nRoot(z, n, [mode])

Q

QuadraticFit([x], y)

QuadraticFitModel([x], y)

QuadraticFitPlot([x], y)

QuarticFit([x], y)

QuarticFitModel([x], y)

QuarticFitPlot([x], y)

Quotient(f(x), g(x))

R

Random(min, max, [size1], [size2])

RealPart(expression)

Remainder(f(x), g(x))

Replace(expression, old, new)

Reshape(matrix)

Return(expression)

Reverse(list)

Right(expression)

RK4(function, t, y, a, b, y0, N=10)

RK45(function, t, y, a, b, y0, Tol=10E-5, hmax=0.25, hmin=10E-6, N=20)

Round(number, digits)

RowReduce(A)

T

Together(expression)

Trace(variable)

Transpose(A)

TriangleWave(x, [T])

TrigConvert(expression)

TrigExpand(expression)

TrigReduce(expression)

V

Variables(expression)

Variance(list)

VectorPlot(list, ...)

VectorPlot3D(list, ...)

W

While(condition)

Z

Zeta(z, [a])