# Question:How to solve 2 ODE equation with Boundary Conditions

## Question:How to solve 2 ODE equation with Boundary Conditions

Maple

Equations

ODES := (diff(f(eta), `\$`(eta, 4)))/((1-phi1)^2.5*(1-phi2)^2.5*((1-phi2)*(1-phi1+phi1*rhos1/rhosf)+phi2*rhos2/rhosf))+S*(f(eta)*(diff(f(eta), `\$`(eta, 3)))-3*(diff(f(eta), `\$`(eta, 2)))-eta*(diff(f(eta), `\$`(eta, 3)))-(diff(f(eta), eta))*(diff(f(eta), `\$`(eta, 2)))) = 0,

(khnf/kf+(4/3)*R)*(diff(theta(eta), `\$`(eta, 2)))/((1-phi2)*(1-phi1+phi1*rhos1*cp1/(rhosf*cpf))+phi2*rhos2*cp2/(rhosf*cpf))+S*Pr*(f(eta)*(diff(theta(eta), eta))-eta*(diff(theta(eta), eta))-gamma*(eta^2*(diff(theta(eta), `\$`(eta, 2)))-2*eta*f(eta)*(diff(theta(eta), `\$`(eta, 2)))-eta*(diff(f(eta), eta))*(diff(theta(eta), eta))+f(eta)*(diff(f(eta), eta))*(diff(theta(eta), eta))+f(eta)^2*(diff(theta(eta), `\$`(eta, 2))))) = 0

Boundary Conditions

f(0) = 0, ((D^2)(f))(0) = 0, (D(theta))(0) = 0, f(1) = 0, (D(f))(1) = 0, theta(1) = 1

phi1 = .1, phi2 = .1, rhos1 = 2720, rhos2 = 2810, rhosf = 997.1, khnf = 1.083061737, kf = .613, cp1 = 893, cp2 = 960, cpf = 4179, Pr = 6.2, knf = .8154646474., S=0.5,R=0.5, gamma=0.5

I am tried to solve it showing following error

Error, (in dsolve/numeric/bvp) matrix is singular

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