Products

	*Mathematica*

		Fast Dense Numerical Linear Algebra
		High-Speed Sparse Linear Algebra
		Large-Scale Linear Systems
		Big-Number Arithmetic
		64-Bit Platform Support
		Faster MathLink
		Numerical Solving of Differential Equations
		Numerical Equation Solving
		Fitting Data
		Numeric Optimization
		`DSolve`
		`RSolve`
		`Reduce`
		`Resolve`
		`FindInstance`
		Symbolic Global Optimization
		Wider Support For Domain Specifications
		Connection Technology
		Importing and Exporting
		Statistical Plots
		Collecting Expressions During Evaluation
		New Linear Algebra Functions
		Algebraic Number Objects
		Authoring and Presentation
		Summary of New Features

Ask about this page

DSolve

The symbolic differential equation solver DSolve has been extended. Key new features include solving classes of mixed systems of differential and algebraic equations (DAEs), and the ability to find all rational solutions to systems of linear differential equations with rational coefficients.

Example: Solving differential-algebraic equations

The solution to the following differential-algebraic equation is fully specified by only one initial value because of the algebraic equation between the variables x(t) and y(t).

${{x(t) -> e^(-2), y(t) -> -e^(-2)}}$

Example: Linear System with Rational Function Coefficients

$DSolve[{u^(t) == ((-t^5 - 3 t^3 + 2 t + 6) u(t))/(t (t^2 - 2 t - 3) (t^3 - 1)) + ... + 1) v(t))/((t + 5) (t^3 - 1)) - (4 t (t^2 - 2 t - 3) u(t))/((t + 5) (t^3 - 1))}, {u(t), v(t)}, t]$

${{u(t) -> ((c_2 t^2)/(t^2 - 2 t - 3)) + ((c_1 t)/(t^2 - 2 t - 3)), v(t) -> ((c_2 t^4)/(t + 5)) + (c_1/(t + 5))}}$

		Documentation from The Mathematica Book Manipulating Integrals in Symbolic Form

		Documentation from the Reference Guide `DSolve`